,13,19,0,0,0,0,Mikami, Y.,,,The Development of Mathematics in China and Japan,,,?,,1912,0,0,,1,,

,19,0,0,0,0,0,Heath, T.L.,,,Diophantus of Alexandria, A study in the History of Greek Algebra,,,?,,1910,59,66,,1,,

,19,0,0,0,0,0,Houzeau de Lehaie, J.Cl.,,,Fragments sur le Calcul numérique,Bull. Acad. Belgique,40,,,1875,455,524,,1,,

,13,29,0,0,0,0,Luroth, J.,,,Vorlesungen über numersichen Rechnen.,,,?,,1900,0,0,,1,,

,19,0,0,0,0,0,Tannery, J.,,,Leçons d'Algèbre et d'Analyse,,,?,,1906,0,0,,1,,

,29,0,0,0,0,0,Hayashi, T.,,,The Bakhshali Manuscript.,,,E. Forsten,Groningen,1995,0,0,,1,0,

,19,0,0,0,0,0,Biernatzki, K.L.,,,Die Arithmetik der Chinesen,J. Reine Angew. Math.,52,,,1856,84,87,,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,La scuola matematica di Bologna,,,Cenno storico,Bologna,1928,0,0,,1,0,

,13,19,0,0,0,0,Bosmans, H.,,,La Théorie des équations dans L' "Invention Nouvelle en l'Algèbre d'Albert Giraud",Mathesis,40,,,1926,59,155,Deals with quadratics and cubics.,1,0,

,19,0,0,0,0,0,Anbouba, A.,,,L'algèbre arabe aux IXe et Xe siecles. Aperçu general.,J. Hist. Arabic Science,2,,,1978,66,100,,1,0,

,10,19,25,0,0,0,Berzolari, L.,,,Enciclopedia Italiana, Vol.2 on Algebra.,,,,Roma,1929,0,0,,1,0,

,19,0,0,0,0,0,Taton, R.,,,A General History of the Sciences. Vol. 1. Ancient and Medieval Science.,,,,Paris,1957,0,0,,1,0,

,19,0,0,0,0,0,Gandz, S.,,,The Algebra of Inheritance…,Osiris,5,,,1938,319,391,,1,0,

,19,0,0,0,0,0,Sarton, G.,,,Introduction to the History of Science,,,,Baltimore,1953,493,0,,1,0,

,13,0,0,0,0,0,Colerus, E.,,,De Pythagore à Hilbert,,,,Paris,1947,98,0,Historical survey (popular).,1,0,

,0,0,0,0,0,0,Wang, Z.,Han, D.,,On dominating sequence method in the point estimate and Smale theorem.,Science in China (Ser. A),33,,,1990,135,144,Smale proved:- Let α^ψ(α)² = q < 1 where ψ(r) = 2r²-4r+1, and α is an expression in the derivatives of f. Then Newton's iteration converges with order 2. We improve on this theorem.,1,0,

,15,0,0,0,0,0,Wang, Z.,Han, D.,Zheng, S.,Convergence on Euler's series: Euler's and Halley's iteration from data at one point,Acta Math. Sinica,33,,,1990,721,738,,1,0,

,3,15,0,0,0,0,Petkovic, M.S.,,,Halley-like Method with Corrections for the Inclusion of Polynomial Zeros,Computing,62,,,1999,69,88,Halley-type iterations for simultaneous inclusion of all zeros with convergence anlaysis for total-step method.,1,0,

,2,16,0,0,0,0,Shub, M.,,,On the work of Steve Smale on the theory of computation, in "From topology to Computation", Ed. M. Hirsch.,,,Springer-Verlag,New York,1993,281,301,Considers complexity of Newton's method.,1,0,

,2,0,0,0,0,0,Smale, S.,,,Newton's method estimates from data at one point, in "The Merging of Disciplines: New Directions in Pure, Applied and Computational Mathematics", Ed. R. Ewing et al.,,,Springer-Verlag,New York,1986,185,196,Gives conditions for z₀ to be an approximate zero of f(z) = 0, I.e. Newton's method converges rapidly to a root from z₀.,1,0,

,3,0,0,0,0,0,Neff, C.,,,Specified Precision Root Finding is in NC,J. Comput. System Sci.,48,,,1994,429,463,Given a polynomial of degree n with integer coefficients bounded by 2ⁿ, let us seek all roots with error < 2^{-μ}. A parallel algorithm is given of time O(log³(n+m+μ)).,1,0,

,1,0,0,0,0,0,Novak, E.,,,Determining zeros of increasing Lipschitz functions,Aequationes Math.,41,,,1991,161,167,Sukharev's variation of the Bisection algorithm is optimal on average.,1,0,

,10,17,0,0,0,0,Burgisser, P.,Clausen, M.,Shokrollahi, M.A.,Algebraic Computational Complexity.,,,Springer-Verlag,Berlin,1997,0,0,Sections on Greatest Common Divisors and evaluation of polynomials that are hard to compute,1,0,

,10,0,0,0,0,0,Collins, G.E.,Johnson, J.R.,Kuchlin, W.,Parallel real roots isolation using the coefficient sign variation method, in "Computer Algebra and Parallelism", Ed. R.E. Zippel,,,Springer-Verlag,New York,1992,71,87,Uses Descartes' rule of signs to search for isolation intervals. Checks initial interval, then bisects and searches left and right subintervals recursively in parallel.,1,0,

,19,0,0,0,0,0,Bradley C.,,,Integer roots of cubic equations.,Math. Gaz.,88,,,2004,508,511,Finds conditions for cubic with integer coefficients to have integer roots.,1,0,

,2,3,0,0,0,0,Sun, F.,Li, X.,,On an accelerating quasi-Newton circular iteration.,Appl. Math. Comput.,106,,,1999,17,29,Describes a parallel iteration in interval arithmetic and investigates its convergence, which is cubic with effectively 4 function evaluations,1,0,

,10,0,0,0,0,0,Cauchy, A.,,,Sur le dénombrement des racines qui, dans une équation algébrique ou transcendente, satisfont àdes conditions données,C.R. Acad. Sci. Paris,40,,,1855,1329,1335,,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Sulla risoluzione apiristica delle congruenze binomie secondo un modulo primo.,Math. Ann.,63,,,1906,54,61,

Solutions of $x^{n}$ ≡a (mod p)

,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Formole di risoluzione della congruenza binomia quadratica e biquadratica,Rend. Accad. Sci. Fis. Mat. Napoli,11,,,1905,13,18,

Solutions of $z^{2}$ ≡q (mod p)

,1,0,

,3,0,0,0,0,0,Petkovic M.,Petkovic L.,Ilic S.,The Guaranteed Convergence of Laguerre-Like Method,Comput. Math. Appl.,46,,,2003,239,251,Gives initial conditions which guarantee convergence of a fourth-order simultaneous method.,1,0,

,10,0,0,0,0,0,Brioschi, M.F.,,,Sur les fonctions de Sturm,C.R. Acad. Sci. Paris,68,,,1869,1318,1321,,1,0,

,17,0,0,0,0,0,Linnainmaa, S.,,,Taylor expansions of the accumulated rounding error,BIT,16,,,1976,146,160,Treats errors in Horner's method for evaluating a polynomial,1,0,

,28,0,0,0,0,0,Aihara,Y.,,,On some inequalities among the roots of an equation and its successive derivatives.,Proc. Phys.-Math. Soc. Japan Ser. 3,16,,,1934,1,6,Let F be an expression involving sums of powers of roots of f and its first 2 derivatives. We show that F may be 0, positive or negative according to the position of the roots.,1,0,

,20,0,0,0,0,0,Sims, C.C.,,,Abstract Algebra, A Computational Approach,,,Wiley,New York,1984,0,0,Section on factorization over finite fields.,1,0,

,13,0,0,0,0,0,Fateman, R.J.,,,Symbolic and Algebraic Computer Programming Systems,SIGSAM Bull.,15,1,,,1981,21,32,Macsyma can factorize certain simple high-degree polynomials such as xⁿ ±1.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,There is no "Uspensky's method", in Proc. 1986 Symp. On Symbolic and Algebraic Computation, Ed. B.W. Char,,,ACM,New York,1986,88,90,We correct the misconception that there exists a method by Uspensky (based on Vincent's theorem) for the isolation of real roots of a polynomial with rational coefficients.,1,0,

,17,0,0,0,0,0,Overill, R.E.,Wilson, S.,,Performance of parallel algorithms for the evaluation of power series.,Parallel Comput.,20,,,1994,1205,1213,,1,0,

,20,0,0,0,0,0,Vandiver, H.S.,,,An Algorithm for the Solution of the Linear Congruence,Amer. Math. Monthly,31,,,1924,137,140,,1,0,

,10,20,0,0,0,0,Winkler, F.,,,Computer Algebra, in "The Encyclopedia of Physical Science and Technology", Ed. R.A. Meyers,,,Academic Press,,1986,0,0,Discusses polynomial remainder siquences for GCD's and Modular GCD algorithms For integral polynomials. Also factorization over finite fields, and Uspensky's algorithm for real roots.,1,0,

,2,0,0,0,0,0,Bergweiler, W.,,,Iteration of meromorphic functions.,Bull. Amer. Math. Soc. (N.S.),29,,,1993,151,188,Considers Julia sets, etc., including Newton's method,1,0,

,2,0,0,0,0,0,Blanchard, P.,,,The dynamics of Newton's method, in "Complex Dynamical Systems, The mathmatics behind the Mandelbrot and Julia sets, Eds. R.L. Devaney et al,,,Amer. Math. Soc.,Providence,1994,139,154,,1,0,

,27,0,0,0,0,0,Bleher, P.,Di, X.,,Correlations between zeros of a random polynomial,J. Stat. Physics,88,,,1997,269,305,Obtains exact analytic expressions for correlation between real zeros of Kac random polynomials. Zeros in (-1,1) are independent of zeros outside this interval.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,On the average number of real roots of a random algebraic equation with dependent coefficients.,J. Indian Math. Soc.,50,,,1986,49,58,When coefficients are dependent with constant correlation the number of real roots is half that when they are independent.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Random polynomials with complex coefficients.,Statist. Probab. Lett.,27,,,1996,347,355,Estimates number of zeros of polynomials with independent random complex coefficients.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Sharp crossings of a non-staionary stochastic process and its application to random polynomials.,Stochastic Anal. Appl.,14,,,1996,89,100,Gives expected number of zeros with slope > u or < -u. This is asymptotically equal to total number of zeros (for fixed u).,1,0,

,27,0,0,0,0,0,Logan, B.F.,Shepp, L.A.,,Real zeros of random polynomials II.,Proc. London Math. Soc.,18,,,1968,308,314,Number of real zeros of a polynomial with normally distributed coefficients has expectation c log n where c depends on the parameter of the distribution.,1,0,

,27,0,0,0,0,0,Miroshin, R.N.,,,Mean number of real zeros of a Gaussian random polynomial with dependent coefficients.,Vestnik Leningrad Univ.,24,1,,,1991,48,55,number of real zeros is a complicated function of correlation coefficient.,1,0,

,27,0,0,0,0,0,Offord, A,C,,,,Lacunary entire functions,Math. Proc. Cambridge Philos. Soc.,114,,,1993,67,83,Lacunary entire functions, like random ones, are large except in very small neighbourhoods of their zeros.,1,0,

,27,0,0,0,0,0,Nayak, N.N.,Mohanty, S.P.,,On the lower bound of the number of real zeros of a random algebraic polynomial.,J. Indian Math. Soc.,49,,,1985,7,15,Gives lower bound for number of zeros when coefficients are dependent random variables.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Shoup, V.,,Fast polynomial factorization over high algebraic extensions of finite fields, in "ISSAC 97. Proc. 1997 Internat. Symp. Symbolic Algebraic Comput.", Ed. W. Kuchlin,,,ACM Press,New York,1997,184,188,

New algorithms factor polynomials of degree n

over field of q elements, where log q = $n^{1 + a},$

$in time O (n^{3 + a + o (1)} + n^{2.69 + 1.69 a})$

,1,0,

,20,0,0,0,0,0,Caris, P.A.,,,A solution of the quadratic congruence modulo p, p = 8n+1, n odd,Amer. Math. Monthly,32,,,1925,294,297,,1,0,

,21,0,0,0,0,0,Zarzo, A.,Dehesa, J.S.,,Spectral Properties of solutions of hypergeometric-type differential equations.,J. Comput. Appl. Math.,50,,,1994,613,623,Gives distribution of zeros of hypergeometric-type functions including classical orthogonal polynomials.,1,0,

,13,0,0,0,0,0,Giventhal, A.B.,,,Manifolds of polynomials having a root of a fixed comultiplicity and the general Newton equation.,Functional Anal. Appl.,16,,,1982,10,14,,1,0,

,13,0,0,0,0,0,Hilbert, D.,,,über die Gleichung neunten Grades.,Math. Ann.,97,,,1927,243,250,,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,Reflections on a pair of theorems by Budan and Fourier.,Math. Mag.,55,5,,,1982,292,298,The theorems considered lead to a method of isolating real roots (Vincent's), which is claimed to be more efficient than Sturm's method.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,A remark on the proposed Syllabus for an AMS short course on Computer Algebra.,SIGSAM Bull.,14,2,,,1980,24,25,There is no Uspensky's method; credit should go to Vincent.,1,0,

,21,0,0,0,0,0,Arriola, E.R.,Zarzo, A.,Dehesa, J.S.,Spectral properties of the biconfluent Heun differential equation,J. Comput. Appl. Math.,37,,,1991,161,169,Gives number of zeros per unit interval of n'th degree Heun polynomials,1,0,

,22,0,0,0,0,0,Akritas, A.G.,Ng, K.H.,,Exact algorithms for polynomial real roots approximation using continued fractions.,Computing,30,,,1983,63,76,Uses infinite precision to solve integer-coefficient polynomial to any required accuracy. Based on Vincent's theorem.,1,0,

,2,12,0,0,0,0,Alefeld, G.,Potra, F.A.,Völker, W.,Effective improvements of the interval-Newton-method, in "Scientific Computing and Validated Numerics", Ed. G. Alefeld et al,,,Akademie-Verlag,Berlin,1996,133,139,Gives methods similar to Interval-Secant and Super-Secant of efficiency up to 1.839. In practise they are not much better than Interval-Newton.,1,0,

,29,0,0,0,0,0,Lang, T.,Montuschi, P.,,Higher Radix Square Root with Prescaling,IEEE Trans. Comput,41,,,1992,996,1009,Prescale to a value close to 1, use a radix-256 one-digit per iteration approach. Hardware oriented.,1,0,

,2,4,7,10,19,20,Bieberbach, L.,Bauer, G.,,Vorlesungen über Algebra,,,Teubner,Leipzig,1933,0,0,Existence, Congruences, Classical Numerical Methods.,1,0,

,2,16,0,0,0,0,Smale, S.,,,Some remarks on the foundations of numerical analysis.,SIAM Rev.,32,,,1990,211,220,Complexity considered briefly.,1,0,

,18,21,0,0,0,0,Van Doorn, E.A.,,,Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tre-diagonal matrices.,J. Approx. Theory,51,,,1987,254,266,,1,0,

,20,0,0,0,0,0,Lord, N.,,,Prime values of polynomials.,Math. Gaz.,79,,,1995,572,573,If p is degree n and is prime for 2n+1 integer values, then p is irreducible.,1,0,

,20,21,0,0,0,0,Gonchar, A.A.,Rakhmanov, E.A.,,Equilibrium measure and distribution of the zeros of extremal polynomials.,Math. USSR Sb.,53,,,1986,119,130,,1,0,

,20,21,0,0,0,0,Rakhmanov, E.A.,,,Equilibrium measure and the distribution of zeros of extremal polynomials of a discrete variable.,Math. Sb.,187,,,1996,1213,1228,,1,0,

,13,0,0,0,0,0,Noether,,,James Joseph Sylvester,Math. Ann.,50,,,1898,138,146,,1,0,

,2,10,0,0,0,0,Moigno,,,Théorèmes de Descartes, de Rolle, de budan et Fourier, de M.M. Sturm et Cauchy.,Nouv. Ann. Math.,3,,,1844,188,194,,1,0,

,20,0,0,0,0,0,Bianchi, L,,,Lezioni sulla Teoria dei Numeri algebrici.,,,Zanichelli,Bologna,1923,87,0,Decomposition into irreducible factors; congruences mod p.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Shoup, V.,,Subquadratic-Time factoring of Polynomials over Finite Fields, in "Proc. 27th Ann. ACM. Symp. On the Theory of Computing",,,ACM Press,,1995,398,406,New probablistic algorithms are presented for factoring polynomials over finite fields in time of order n to the power 1.815. They rely on fast matrix multiplication techniques.,1,0,

,13,0,0,0,0,0,Furstenau, E.,,,Neue Methode zur Darstellung und Berechnung der imaginaren Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten,Schrift. Ges. Bef. Ges. Naturwiss. Marburg,9,,,1871,19,48,,1,0,

,3,0,0,0,0,0,Kirrinnis, P.,,,Fast Numerical Improvement of Factors of Polynomials and of Partial Fractions, in "Proc. 1998 Intern. Symp. On Symbolic and Algebraic Computation", Ed. O. Gloor,,,ACM Press,,1998,260,267,Uses multidimensional Newton iteration applied to the coefficient vectors. Provides starting value conditions and time bounds.,1,0,

,13,0,0,0,0,0,McNamee, J.M.,,,An updated supplementary bibliography on roots of polynomials.,J. Comput. Appl. Math.,110,,,1999,305,306,Covers the period roughly 1993-1999, plus many earlier ones. On Web.,1,0,

,10,0,0,0,0,0,Chin, P.,Corless, R.M.,Corliss, G.F.,Optimization Strategies for the Approximate GCD Problem, in "Proc. 1998 Intern. Symp. On Symbolic and Algebraic Computation-ISSAC98", Ed. O. Gloor,,,ACM Press,,1998,228,235,,1,0,

,27,0,0,0,0,0,Odoni, R.W.K.,,,Zeros of random polynomials over a finite field.,Math. Proc. Cambridge. Philos. Soc.,111,,,1992,193,197,,1,0,

,27,0,0,0,0,0,Panda, R.K.,Pratihari, D.,Pattanaik, B.P.,On the number of real roots of a random algebraic equation.,J. Austral. Math. Soc. (Ser. A),54,,,1993,86,96,,1,0,

,27,0,0,0,0,0,Pratihari, D.,Pattanaik, B.P.,,On the lower bound of the number of real roots of random algebraic equations.,Bull. Inst. Math. Acad. Sinica,19,,,1991,251,260,,1,0,

,27,0,0,0,0,0,Sambandham, M.,,,On the average number of real zeros of a class of random algebraic curves.,Pacific J. Math.,81,,,1979,207,215,Gives upper bound on number of real roots where coefficients are dependent.,1,0,

,11,0,0,0,0,0,Soh C.B.,,,Generalization of the Hermite-Behler Theorem and application,IEEE Trans. Automat. Control,35(2),,,1990,222,225,,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,Real zeros of a random algebraic polynomial.,Quart. J. Math. Oxford,24,,,1973,169,175,Gives lower bound for number of real roots for polynomial whose coefficents have specified range of variance and third moment.,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,On the upper bound of the number of real roots of a random algebraic equation with infinite variance II.,Proc. Amer. Math. Soc.,44,,,1974,446,448,450,1,0,

,27,0,0,0,0,0,Uno, T.,,,On the lower bound of the number of real roots of a random algebraic equation,Statist. Probab. Lett.,30,,,1996,157,163,The coefficients are dependent Gaussian random variables.,1,0,

,27,0,0,0,0,0,Shenker, M.,,,The mean number of real roots for one class of random polynomials.,Ann. Probab.,9,,,1981,510,512,For low correlation between random Gaussian coefficients, the number of roots is the same as if correlation were zero.,1,0,

,13,0,0,0,0,0,Bellavitis, G.,,,Risoluzione numerica delle equazioni.,Mem. Reale Ist. Veneto Sci. Let. Arti,6,,,1857,357,413,,1,0,,p> ,0,21,0,0,0,0,Kuijlaars, A.B.J.,Rakhmanov, E.A.,,corr. To "Zero distributions to discrete orthogonal polynomials" (JCAM 99 255),J. Comput. Appl. Math.,104,,,1999,213,213,Theorem 7.1 of original paper is incorrect.,1,0,

,15,0,0,0,0,0,Drakopoulos, V.,Argyropoulos,N.,Bohm, A.,Generalized computation of Schröder iteration functions to motivate families of Julia and Mandelbrot-like sets.,SIAM J. Numer. Anal.,36,,,1999,417,435,Gives a new algorithm to generate the Schröder functions and maximize their efficiency, Describes Julia sets related to a particular cubic.,1,0,

,21,0,0,0,0,0,He, M.,,,The faber polynomials for circular arcs, in "The mathematics of Computation 1943-1993". Ed. W. Gautschi,,,Amer. Math. Soc.,Providence, RI,1995,301,304,let E be a set, and w = Φ(z) be a conformal mapping of C\E to exterior of circle |w| = PE. Then with certain conditions Φ(z) = z + a₀+a₁/z+.. F_n = polynomial part of {Φ(z)}ⁿ, is Faber polynomial of degree n generated by E. Studies Faber polynomials associated with a circular arc, as well as zeros of these polynomials.,1,0,

,1,2,10,14,0,0,Reverchon, A.,Ducamp, ??,,Mathematical Software Tools in C++,,,Wiley,,1993,0,0,Treats Bisection, Newton's and Bairstow's methods. Also greatest common divisors.,1,0,

,13,0,0,0,0,0,Schnuse, C.H.,,,Die theorie und Auflösung der höheren algebraischen und der transcendente Gleichungen.,,,Braunschweig,,1850,0,0,,1,0,,p> ,15,0,0,0,0,0,Yao, Q.,,,On Halley Iteration,Numer. Math.,81,,,1999,647,677,We exhibit the non-overshoot property (will not skip over m zeros) of halley's iteration and also its monotonic convergence to real roots.,1,0,

,1,2,7,0,0,0,Woodford, C.,Phillips, C.,,Numerical Methods with Worked Examples,,,Chapman & Hall,,1997,0,0,treats Bisection, Newton and Secant methods,1,0,

,19,25,0,0,0,0,Varadarajan, V.S.,,,Algebra in Ancient and Modern Times,,,Amer. Math. Soc.,Providence, RI,1998,0,0,Treats cubic and biquadratic equations (Cardano etc) and fundamental theorem of algebra,1,0,

,2,10,13,0,0,0,Torii, T.,Sakurai, T.,Suguira, H.,An Application of Sunzi's Theorem for Solving Algebraic Equations, in "Proc. First China-Japan Seminar on Numerical Mathematics", Ed. Z.-C. Shi and T. Ushijama,,,World Scientific,Singapore,1993,155,167,Method based on Newton, Sturm sequences, etc.,1,0,

,15,0,0,0,0,0,Wang, X.H.,Han, D.,,The Global Convergence of a Family of Iterations, in "Proc. First China-Japan Seminar on Numerical Mathematics", Ed. Z.-C. Shi and T. Ushijama,,,World Scientific,Singapore,1993,230,233,Methods based on high-order derivatives.,1,0,

,29,0,0,0,0,0,Werthum,,,Die Arithmetik des Elia Misrachi,,,,,1849,0,0,Treats square and cube roots,1,0,

,10,0,0,0,0,0,Hattensdorffs, K.,,,Die Sturmschen Funktionen,,,,Hannover,1874,0,0,Describes Sturm's theorem and related matters,1,0,

,10,0,0,0,0,0,Balinski, A.I.,Podlevski, B.M.,,Computaional Aspects of the Application of Frobenius Matrix to Separation of Roots of Polynomials,Comput. Math. Math. Phys.,39,,,1999,1029,1033,Considers Bezoutian matrix (resultant) of two polynomials, and conditions that they have common roots.,1,0,

,19,0,0,0,0,0,Zhi, L.,Liu, Z.,,P-Irreducibility of Binding Polynomials,Computers Math. Applic.,38 2,,,1999,1,10,Gives conditions, for degree 3 and 4, that a polynomial with positive coefficients can be factored (or not) into polynomials with same property.,1,0,

,1,2,7,14,15,17,Schwarz, H.R.,,,Numerical Analysis: A Comprehensive Introduction,,,Wiley,Chichester,1989,0,0,Standard text-book treatment of Bisection, Newton, Secant, Evaluation, Muller.,1,0,

,10,0,0,0,0,0,Locher, F.,Skrzipek, M.-R.,,A stability test for complex polynomials,Analysis,15,,,1995,205,219,Uses argument principle and Sturm sequences to find the number of zeros inside the unit circle or the unimodular zeros.,1,0,

,20,0,0,0,0,0,Itoh, T.,,,An Efficient Probabilistic Algorithm for Solving Quadratic Equation over Finite Fields,Electron. Commun. Japan (part 3),72,3,,,1989,88,96,Proposes a probabilistic algorithm in which the probability that the desired solution is obtained by one application is kept as one-half and the quadratic equation is solved more efficiently than by Rabin's method.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Random Polynomials,Appl. Math. Lett.,3,2,,,1990,43,46,The behaviour of an algebraic and a trigonometric polynomial is reviewed, and the number of times that the curve representing these polynomials cross any real line in the xy-plane is presented.,1,0,

,5,12,0,0,0,0,Schaeffer, M.J.,,,Precise Zeros of Analytic Functions Using Interval Mathematics,Interval Computations,4,,,1993,22,39,An interval arithmetic algorithm for the computation of zeros of an analytic function inside a rectangle is presented. It is based on the argument principle, is guaranteed to converge, and has a specified accuracy.,1,0,

,17,0,0,0,0,0,Pan, V.Y.,et al,,Fast multipoint polynomial evaluation and interpolation via computations with structured matrices,Ann. Numer. Math.,4,,,1997,483,510,Considers multipoint polynomial evaluation via FFT. Extended to Chebyshev representation.,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Sulla risoluzione aparistica delle congruenze binomie,Atti. R. Accad. . Lincei Rend. Ser. 5,16,,,1907,603,608,

Solves $z^{n}$ ≡a (mod p)

,1,0,

,20,29,0,0,0,0,Capelli, A,,,Sulla riduttibilita della funcione $x^{n}$ -A in un campo qualunque.,Math. Ann.,54,,,1901,602,603,,1,0,

,17,0,0,0,0,0,Reif, J.H.,,,Approximate complex polynomial evaluation in near constant work per point, in "Proc. 29th Annual ACM Symp. On Theory of Computing".,,,ACM Press,New York,1997,30,39,

Let k = log(|P|/ε) where |P| = Σ| $a_{i} |; ϵ = bound on evaluation error . We evaluate P at m≥nlogn / \log^{2} k$

$points in O (\log^{2} logn) work per point . For special points used in signal processing$

$the work is even less .$

,1,0,

,19,0,0,0,0,0,Rose, P.,,,The Italian Renaisssance of Mathematics,,,Librarie Droz,Geneva,1975,0,0,Treats early solution of cubic and quartic (Cardan, Tartaglia, etc),1,0,

,20,0,0,0,0,0,Manove, M.,Bloom, S.,Engelman, C.,Rational functions in MATLAB, in "Symbolic Manipulation Languages and Techniques", Ed. D.G. Bobrow,,,North Holland,Amsterdam,1968,86,102,Deals with factorization of polynomials with integer coefficients into polynomials irreducible over the integers.,1,0,

,3,0,0,0,0,0,Petkovic, M.S.,Ilic, S.,,Point estimation and the convergence of the Ehrlich-Aberth method,Publ. Inst. Math.,62,,,1997,141,149,Considers the Ehrlich-Aberth method for simultaneous approximation of simple zeros, and initial conditions which enable safe convergence.,1,0,

,20,0,0,0,0,0,Pohst, M.,Zassenhaus, H.,,Algorithmic Algebraic Number Theory,,,Cambridge Univ. Press,London,1989,69,86,Considers factorizing polynomial over finite field into irreducible factors.,1,0,

,2,0,0,0,0,0,Kirrinnis, P.,,,Newton Iteration Towards a Cluster of Polynomial Zeros, in "Foundations of Computational Mathematics", Ed. F. Cucker and M. Shub.,,,Springer-Verlag,New York,1997,193,215,Coefficient of factor corresponding to a roots cluster are computed using Newton iteration in C to the power k. The starting value condition is very restrictive.,1,0,

,29,0,0,0,0,0,Ashenhurst, R.L.,,,Function evaluation in unnormalized arithmetic.,J. Assoc. Comput. Mach.,11,,,1964,168,187,Section on square root.,1,0,

,20,29,0,0,0,0,Fitch, J.,,,A Simple Method of Taking nth Roots of Integers,SIGSAM Bull.,8,no. 4,,,1974,26,26,Uses Newton's method, where only interested in case where root is itself an integer,1,0,

,20,0,0,0,0,0,Schwartz, S.,,,Contribution à la réductibilité des polynômes dans la théorie des congruences.,Ceska Spol. Nauk. Trida Mat.-Pri. Vest. Prague,,,,1939,1,7,,1,0,

,3,0,0,0,0,0,Petkovic, M.,Herceg, D.,,Borsch-Supan-like methods:Point estimation and parallel implementation.,Internat. J. Comput. Math.,64,,,1997,327,341,Gives initial condition for convergence of Borsch-Supan method and its Weierstrass modification for simultaneous approximation of zeros. Compares the methods on parallel computers.,1,0,

,20,0,0,0,0,0,Gianni, P.,Trager, B.,,Square-free Algorithms in Positive Charactersitic,Applic. Alg. Eng. Comm. Comput.,7,,,1996,1,14,We study the problem of the computation of the square-free decomposition for polynomials over fields of positive characteristic.,1,0,

,20,25,0,0,0,0,Mines, R.,Richman, F.,Ruitenberg, W.,A Course in Constructive Algebra,,,Springer-Verlag,Berlin,1988,0,0,Treats factorization into irreducible factors and fundamental theorem.,1,0,

,25,0,0,0,0,0,Frohlich, A.,Sheperdson, J.C.,,Effective Procedures in Field Theory,Philos. Trans. Roy. Soc. London Ser. A,248,,,1956,407,432,Treats existence of splitting algorithms.,1,0,

,13,19,0,0,0,0,De. Morgan,,,Budget of Paradoxes,,,,,1872,292,375,Treats Horner's method,1,0,

,10,19,0,0,0,0,Perkins, G.R.,,,Treatise on Algebra,,,,New York,1842,0,0,,1,0,

,27,0,0,0,0,0,Hirata, H.,,,Macro-Properties of Real Roots of a Random Algebraic Equation,J. Fac. Eng. Chiba Univ.,38,,,1980,35,42,The distribution of the real roots of a random algebraic equation, whose coefficients are dependent normal random variables with arbitrary mean, covariance and variance, are studied.,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Location of the zeros of polynomials satisfying three-term recurrence relations with complex coefficients,Integral Trans. Spec. Functions,2,,,1994,267,278,The method leads to the exact interval where all zeros of classical polynomials are located.,1,0,

,19,0,0,0,0,0,Lewy, H.,,,Studies in assyro-babylonian mathematics and Metrology,Orientalia,18,,,1949,40,67,,1,0,

,2,15,19,0,0,0,Nordgaard, M.A.,,,A historical survey of algebraic methods of approximating the roots of numerical higher equations up to the year 1819.,,,Teachers College,,Columbia Univ., NY,1922,0,0,Covers early history of methods such as Regula Falsi, Vieta's, Newton-Raphson, Halley, Horner's,1,0,

,1,2,17,0,0,0,Dorn, W.,McCracken, D.,,Numerical Methods with FORTRAN IV Case Studies,,,Wiley,New York,1972,0,0,Considers Newton, Bisection, Successive Approximation, and Horner's method.,1,0,

,19,0,0,0,0,0,Sayyid Taha Baqir,,,Old Babylonian problem texts found in Tell Harmal,Sumer,6,,,1950,130,148,Gave solution to quadratic (probably the earliest).,1,0,

,29,0,0,0,0,0,Sachs, A.,,,Babylonian Mathematical Texts II-III,J. Cunieform Studies,6,,,1952,151,156,Babylonians gave method for cube root.,1,0,

,19,0,0,0,0,0,Miller G.A.,,,The Oldest Extant mathematics,School & Society,35,,,1932,833,834,Babylonians had formula similar to modern ones for roots of a quadratic.,1,0,

,29,0,0,0,0,0,Darboux, G.,,,Sur l'extraction de la racine carré,Bull. Sci. Math. Ser. 2,11,,,1887,176,184,Square roots.,1,0,

,28,0,0,0,0,0,Ahmad, M,,,On polynomials with real zeros,Canad. Math. Bull.,11,,,1968,237,240,Considers roots of a polynomial and its derivative.,1,0,

,21,0,0,0,0,0,Dilcher, K.,Nulton, J.D.,Stolarsky, K.B.,The zeros of a certain family of trinomials,Glasgow Math. J.,34,,,1992,55,74,GET THIS,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,On zeros of derivatives of polynomials.,Canad. Math. Bull.,11,,,1968,443,445,GET THIS,1,0,

,18,28,0,0,0,0,Sz.-Nagy, B.,,,über algebraische Gleichungen mit lauter reellen Wurzeln.,Jahresber. Deutsch. Math.-Verein.,27,,,1918,37,43,,1,0,

,27,21,0,0,0,0,Das, M.,,,Real zeros of a random sum of orthogonal polynomials,Proc. Amer. Math. Soc.,27,,,1971,147,153,

Let $P_{k}^{*} (x) be normalized Legendre polynomials, then average number of zeros$

$c_{0} P_{0}^{*} + . . . + c_{n} P_{n}^{*} in [- 1,1] is asymptotically \frac{n}{\sqrt{3}}, for large n .$ ,1,0,

,21,27,0,0,0,0,Das, M.,Bhatt, S.S.,,Real roots of random harmonic equations,Indian J. Pure Appl. Math.,13,,,1982,411,420,

Let $ϕ_{k} (k = 0, . ., n) be a sequence of classical orthogonal polynomials, and c_{0}, . . . c_{n}$

be independent normal random variables, and $a_{0}, . . ., a_{n} normalizing constants in a certain sense . The expectation of real zeros of$

Σ $c_{k} a_{k} ϕ_{k} = \frac{n}{\sqrt{3}} as n \to \infty .$

,1,0,

,22,0,0,0,0,0,Chen, J.,,,A new algorithm for the isolation of the real roots of polynomial equations, in "Second Intern. Conf. On computers and Applications",,,,Beijing, China,1987,714,719,Isolates multiple real roots of polynomials with integer coefficients. Uses Vincent's theorem and continued fractions. Time O(n³L³(|p₀|)) where L(integer) = Log(abs(integer)), |p₀|=largest coefficient of polynomial.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,On the average number of crossings of an algebraic polynomial,Indian J. Pure Appl. Math.,20,,,1989,1,9,

If P(x) = $Σ_{0}^{n - 1} a_{i} x^{i}, where the a_{i}$ are standard normal random variables, and $\frac{m^{2}}{n}$ →0 as

n→∞, the expectation of the number of real roots of P(x) = mx ∼ $\frac{1}{π} \log ($ n/ $m^{2}) if$

m tends to infinity with n or approaches( log n)/π if m bounded.

,1,0,

,21,27,0,0,0,0,Farahmand, K.,,,Level crossings of a random orthogonal polynomial.,Analysis,16,,,1996,245,253,

Gives asymptotic estimate of number of K-level crossings of a random combination of Legendre polynomials.The number → $\frac{n}{\sqrt{3}}$ provided ( $K^{2} / n)$ → 0 as n → ∞,1,0,

,25,0,0,0,0,0,Loria,,,Sur une démonstration du théorème fondamental de la théorie des équations algébriques.,Acta Math.,9,,,1886,71,0,An article by Holst in the preceding year is very similar to one by Mourey in 1828 (concerning existence of solutions).,1,0,

,25,0,0,0,0,0,Cauchy, A.L.,,,Sur les racines imaginaires des équations.,J. Ecole Poly.,18,,,1820,411,416,,1,0,

,25,0,0,0,0,0,Burg, A.,,,Ueber die Existenz der Wurzeln einer höhern Gleichung mit einer Unbekannten.,J. Reine Angew. Math.,5,,,1830,182,184,186,1,0,

,27,0,0,0,0,0,Glendinning, R.,,,The growth of the expected number of real zeros of a random polynomial.,J. Austral. Math. Soc. (Ser. A),46,,,1989,100,121,Let X₀,…,X_n be a stationary Gaussian process. We give conditions for expected number of real zeros of ΣX_jz^j to be (2 log n)/π as n → ∞,1,0,,p> ,27,0,0,0,0,0,Glendinning, R.,,,The growth of the expected number of real zeros of a random polynomial with dependent coefficients.,Math. Proc. Cambridge Philos. Soc.,104,,,1988,547,559,If coefficients form a stationary uniformly mixing sequence, then expected number of real zeros in [0,1] ∼ (logn)/(2π). As n → ∞,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,On the upper bound of the number of real roots of a random algebraic equation with infinite variance.,J. London Math. Soc.,6,,,1973,598,604,Number usually ≤ μ(log n)²,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Crossing of a random algebraic polynomial.,Indian J. Pure Appl. Math.,21(2),,,1990,109,115,,1,0,

,27,0,0,0,0,0,Farahmand, K,,,Exceedence measure of random polynomials.,Indian J. Pure Appl. Math.,26(9),,,1995,897,907,,1,0,

,19,0,0,0,0,0,Needham, Joseph,,,Science and Civilization in China,,III,Cambridge Univ Press,,1954,0,0,,1,0,

,2,0,0,0,0,0,von Haeseler, F.,Peitgen, H.O.,,Newton's method and complex dynamical systems,Acta Appl. Math.,13,,,1988,3,58,Considers Basins of attraction for Newton's method, including a historical survey, & reference to Julia and Mandelbrot sets. Also in "Newton's Method and Dynamical Systems", ed. H.O. Peitgen, Kluwer, Dordrecht, (1989),1,0,

,2,0,0,0,0,0,Hurley, M.,,,Multiple Attractors in Newton's Method,Ergodic Theory Dynamical Systems,6,,,1986,561,569,If d>=2, exists a polynomial of degree d so that its Newton function has 2d-2 periodic attractors.,1,0,

,18,0,0,0,0,0,Sylvester,J. J.,,,"Algebraical Researches containing a disquisition on Newton's Rule for the Discovery of Imaginary Roots,…,Philos.Trans. Roy. Soc. London,154,,,1864,579,666,Gives lower bound to number of imaginary roots of equation up to 5th degree, etc.,1,0,

,18,0,0,0,0,0,Sylvester, J.J.,,,"On the explicit values of Sturm's Quotients",Phil. Mag. Ser. 4,6,,,1853,293,296,,1,0,

,17,0,0,0,0,0,Miklosko, J.,,,Complexity of Parallel Algorithms in "Algorithms, Software and Hardware of Parallel Computers", eds. J. Miklosko and V.E. Kotov,,,Springer,Berlin,1984,47,48,Gives parallel algorithm for evaluating a polynomial,1,0,

,25,0,0,0,0,0,Bishop, E.,,,Foundations of constructive analysis,,,McGraw-Hill,,1967,0,0,Proves Fundamental Theorem,1,0,

,29,0,0,0,0,0,Ch'u-chung, Ting,,,Pai-fu-t'ang Mathematical Collections,,,,,1876,0,0,,1,0,

,13,0,0,0,0,0,Aki-ko, Taira,,,Sampo Shojo or Maiden's Arithmetic,,,,Japan,1774,0,0,,1,0,

,0,20,0,0,0,0,Dirichlet-Dedekind,,,Zahlentheorie,,,,,1968,,,Considers quadratic congruences,1,0,

,7,0,0,0,0,0,Coreless, R.M.,,,Cofactor iteration,SIGSAM Bull.,30(1),,,1996,34,38,Finds GCD of approximately known pair of polynomials.,1,0,

,10,0,0,0,0,0,Emiris, I.Z.,Galligo, A.,Lombardi, H.,Certified approximate univariate GCD's.,J. Pure and Applied Algebra,117-8,,,1997,229,251,Uses SVD,1,0,

,10,0,0,0,0,0,Karmarkar, N.,Lakshman, Y.N.,,Approximate polynomial greatest common divisors and nearest singular polynomials in Proc. Internat. Symp. On Symbolic and Algebraic Comput. (ISSAC),Y.N. Lakshman ed.,,,ACM Press,New York,1996,35,39,,1,0,

,25,0,0,0,0,0,Laisant, C.A.,,,Démonstration nouvelle du théorème fondamental de la théorie des équations,Bull. Soc. Math. France,15,,,1887,42,44,Fundamental Theorem of Algebra,1,0,

,29,0,0,0,0,0,Breuer, S.,Zwas, G.,,Numerical Mathematics- a Laboratory Approach,,,Cambridge Univ. Press,,1993,0,0,An excellent treatment of square and cube roots, including third order methods based on Halley etc.,1,0,

,20,0,0,0,0,0,Roelse, P.,,,Factoring high-degree polynomials over F₂ with Niederreiter's algorithm on the IBM SP2,Math. Comp.,68,,,1999,869,880,Involves setting up and solving a system of linear equations, which is performed in parallel. A new record is set.,1,0,

,19,29,0,0,0,0,Labat, R.,,,La Mesopotamie,,,Press Univ. de France,,1957,113,114,Babylonians found $\sqrt{2}$ to 6D, and solved quadratics.,1,0,

,7,0,0,0,0,0,Zou, X,,,Analysis of the quasi-Laguerre method,Numer. Math.,82,,,1999,491,519,Variation of Laguerre's method without using second derivatives. Order 1+ $\sqrt{2}$ . In some cases convergence guaranteed.,1,0,

,10,0,0,0,0,0,Krandick, W.,,,Isolierung reeler Nullstellen von Polynomen, in "Wissenschaftliches Rechnen", ed. J. Herzberger,,,Akademie Verlag,Berlin,1905,105,0,Uses Descartes' rule,1,0,

,10,20,0,0,0,0,Lipson, J.D.,,,Elements of Algebraic Computing,,,Addison-Wesley,,1981,0,0,Treats Root-finding over Power Series Domains,1,0,

,19,0,0,0,0,0,Van Der Waerden, B.L.,,,Science Awakening,,,,Groningen,1954,,0,Cubics among Babylonians,1,0,

,27,0,0,0,0,0,Leadbetter, M.R.,,,On Crossing of levels and curves by a wide class of stochastic processes.,Ann. Math.Statist.,37,,,1966,260,267,Shows that tangencies have probability 0.,1,0,

,27,0,0,0,0,0,Leadbetter, M.R.,Cryer, J.D.,,The variance of the number of zeros of a stationary normal process.,Bull. Amer. Math. Soc.,71,,,1965,561,563,,1,0,

,27,0,0,0,0,0,Ylvisaker, N.D.,,,The expected number of real zeros of a stationary Gaussian process..,Ann. Math.Statist.,36,,,1965,1043,1046,,1,0,

,29,19,0,0,0,0,Datta, B.,Singh, A.N.,,History of Hindu mathematics, I and II,,,Asia Publishing House,,1962,0,0,Deals with square and cube roots, quadratic equations,1,0,

,29,0,0,0,0,0,Kaye, G.R.,,,Indian Mathematics,Isis,2,,,1919,327,356,Square roots.,1,0,

,19,29,0,0,0,0,Kaye, G.R.,,,The Bakshali Manuscript: A Study in Medieval Mathematics.,,43,Archeol. Survey of india,New Delhi,1981,0,0,Quadratics & Square roots,1,0,

,19,2,0,0,0,0,Burton, D.M.,,,The History of Mathematics, an Introduction,,,Allyn & Bacon,Boston,1986,0,0,Treats cubics & quadratics Cardan etc.,1,0,

,19,0,0,0,0,0,Heath, T.L.,,,The Thirteen Books of Euclid's Elements,,,Cambridge Univ. Press,,1926,0,0,Gives geometric solution of quadratics.,1,0,

,28,0,0,0,0,0,Cayley, A.,,,Sur les Racines D'une Équation Algébrique,C.R. Acad. Sci. Paris,110,,,1890,174,176,Show that if f'(x)=0 has n-1 roots, then f(x)=0 has n.,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,Span of derivatives of polynomials,Amer. Math. Monthly,74,,,1967,527,531,Let σ(p) = max real root-min real root, where roots all real. Proves that, if roots also positive, their sum ≤1/n, and k≤n-2, then max(σ(p^(k)))=n-k. Also a similar result for Σx_i²≤1/n.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,A Short Note on a New Method for Polynomial Real Root Isolation.,SIGSAM Bull.,12(4),,,1978,12,13,Based on Vincent's method for isolating real roots by continued fractions. Order of n⁵,1,0,

,21,27,0,0,0,0,Das, M.,,,Real zeros of a random sum of orthogonal polynomials.,Proc. Amer. Math. Soc.,27,,,1971,147,153,Let c_i be random variables with expectation zero and variance 1, P_k^* be Legendre polynomials, then Σ₀ⁿP_k^* has average number of zeros ∼ n/ $\sqrt{3}$ ,1,0,

,27,0,0,0,0,0,Mishra, M.N.,Nayak, N.N.,Pattanayak,S.,Strong results for real zeros of random polynomials,Pacific J. Math,103,,,1982,509,522,,1,0,

,29,0,0,0,0,0,Ayyangar,,,The Bakhshali Manuscript,Mathematics Student,7,,Madras, India,1939,1,16,Treats square roots.,1,0,

,13,0,0,0,0,0,Rolle, M.,,,Demonstratio d'une Méthode pour Résoudre les Égalites de toutes Degrez,,,,,1691,0,0,,1,0,

,13,0,0,0,0,0,Delagny,,,Analyse Générale,,,,Paris,1733,0,0,,1,0,

,19,0,0,0,0,0,Cardan, G.,,,Arithmetic,,,,,1550,0,0,Section on square and cube roots,1,0,

,13,0,0,0,0,0,Legebeke, G.J.,,,Eene Eigenschap van de Wortels Eener Afgeleide Vergelijking,Nieuw Archief Voor Wiskunde (Ser. 1),8,,,1881,75,80,,1,0,

,29,0,0,0,0,0,Gupta, R.C.,,,Baudhayana's Value of $\sqrt{2}$ ,Mathematics Education,6,,,1972,77,79,Gives ancient derivation of $\sqrt{2}$ , accurate to 5D.,1,0,

,10,0,0,0,0,0,Cajori, F.,,,On Michel Rolle's book "Méthode pour résoudre les egalitez" and the history of "Rolle's theorem".,Bibl. Math. (Ser. 3),12,,,1911,300,313,Method similar to Sturm's sequences,1,0,

,13,0,0,0,0,0,Van Den Berg, F.J.,,,Over Het Verband Tusschen de Wortels Eener Vergelijking en die van Hare Afgeleide.,Nieuw Arch. Wisk. (Ser. 1),9,,,1882,1,14,,1,0,

,25,0,0,0,0,0,Macnie, J.,,,Proof of the theorem that every equation has a root,The Analyst,5,,,1878,80,82,,1,0,

,25,0,0,0,0,0,Mertens, F.,,,Der Fundamentalsatz der Algebra,Mon. Math. Phys.,3,,,1892,293,308,,1,0,

,1,2,7,10,0,0,Nonweiler, T.R.F.,,,Computational Mathematics-An Introduction to Numerical Approximation,,,Ellis Horwood,Chichester,1984,0,0,Standard treatment of Bisection, Newton, Secant, Sturm,1,0,

,16,0,0,0,0,0,Petkovic, M.S.,Petkovic, L.D.,,On bounds of the R-order of some iterative methods,Z. Angew. Math. Mech.,69 T,,,1989,197,198,,1,0,

,29,0,0,0,0,0,Channabasappa, M.N.,,,The Bakhshali Square-Root Formula and High-Speed Computation,Ganita Bharati,1,,,1979,25,27,It is more efficient than Newton's square-root method,1,0,

,20,0,0,0,0,0,Schwarz, St.,,,Contribution a la réductibilté des polynômes dans la théorie des congruences,Ceska Spol. Prague, Trida Math.-Prir. Vest.,,,,1939,1,7,Relates irreducible factors to a characteristic polynomial,1,0,

,3,5,0,0,0,0,Wang, X.,Xuan, X.,,Random Polynomial Space and Computational Complexity Theory,Sci. Sinica (Ser. A) Math. Phys. Astr. Tech. Sci.,30,,,1987,673,684,Recommends Lehmer's method with parallel disk iteration.,1,0,

,29,0,0,0,0,0,Enestrom, G.,,,Une note dans M. Cantor…,Bibl. Math. Ser. 3,8,,,0,412,413,Deals with cube roots,1,0,

,20,0,0,0,0,0,Maller, M.,Whitehead, J.,,Efficient p-adic Cell Decomposition for Univariate Polynomials,J. Complexity,15,,,1999,513,525,Finite fields,1,0,

,19,29,0,0,0,0,Elfering, K.,,,Die Mathematik des Aryabhata I,,,Wilhelm Fink Verlag,Munich,1975,0,0,Gives details of square and cube roots, and quadratic, as computed in early India.,1,0,

,2,0,0,0,0,0,Fouret, G.F.,,,Sur la Méthode d'approximation de Newton,Nouv. Ann. Math.,,,,1890,567,585,Treats Newton's method,1,0,

,19,0,0,0,0,0,Savasordo, A.,,,Liber embadorum,,,??,??,1145,0,0,Brought Arabic solution of quadratic to the West.,1,0,

,19,0,0,0,0,0,Pacioli, L.,,,Summa de Arithmetica Geometria Proportioni et Proportionalita,,,??,>>,1494,0,0,deals with quadratics,1,0,

,19,0,0,0,0,0,Stevin, S.,,,L'Arithmétique,,,,,1585,0,0,Reduces all quadratics to a single type,1,0,

,19,0,0,0,0,0,Stifel, M.,,,Die Coss,,,,,1524,0,0,Considers negative roots of quadratic,1,0,

,19,0,0,0,0,0,Stifel, M.,,,Arithmetica Integra,,,,,1544,0,0,quadratic,1,0,

,25,0,0,0,0,0,Enriques, F.,,,Questioni riguardanti le matematiche elementari Vol. I,,,,Bologna,1912,547,561,Considers fundamental theorem of algebra (existence of roots),1,0,

,25,0,0,0,0,0,Ko, K.,,,Complexity Theory of Real Functions,,,Birkhauser,Boston,1991,0,0,Section on existence and computability of roots of functions,1,0,

,28,0,0,0,0,0,Horwitz, A.,,,On the Ratio Vectors of Polynomials,J. Math. Anal. Appl.,205,,,1997,568,576,Relation between roots of a polynomial and its derivative, when the polynomial has all real roots,1,0,

,25,0,0,0,0,0,Sigrist,,,Equations of prime degree: Problem 88-4 by E. Galois,Math. Intelligencer,11,,,1989,53,54,proves that an equation of prime degree is solvable by radicals iff all its roots are rational functions of any 2 of them.,1,0,

,19,0,0,0,0,0,Patterson, W.M.,Lubecke, A.M.,,A special circle for quadratic equations.,Math. Teacher,84,,,1991,125,127,Gives graphical method for roots of quadratic.,1,0,

,19,0,0,0,0,0,Feser, V.G.,,,Special circle II.,Math. Teacher,85,,,1992,173,174,Gives history of a graphical method for a quadratic.,1,0,

,19,0,0,0,0,0,Pope, C.,,,Special circle I.,Math. Teacher,85,,,1992,173,0,Gives history of a graphical method for a quadratic.,1,0,

,19,0,0,0,0,0,Holmes, C.R.,,,Imagine the roots of a quadratic.,Math. Gaz.,74,,,1990,285,286,Way of "seeing" graphically the imaginary roots of a quadratic.,1,0,

,29,0,0,0,0,0,Brown, l.M.,,,An algorithm for square roots: an episode in the campaign against dotage.,Math. Gaz.,81,,,1997,428,0,Gives a new formula for square root.,1,0,

,29,0,0,0,0,0,Cortadella, J.,Lang, T.,,High-radix Division and Square Root with Speculation,IEEE Trans. Computers,43,,,1994,919,931,One digit produced per iteration,1,0,

,2,0,0,0,0,0,Ford, W.F.,Pennline, J.A.,,Accelerated convergence in Newton's method,SIAM Rev.,38,,,1996,658,659,Modifies Newton's method using N'th root of f', to achieve N'th order convergence,1,0,

,4,0,0,0,0,0,Willers, F.A.,,,Rechenkontrollen und Reschenschemata zum Graeffeschen Verfahren,Wiss. Zeit. Tech. Hochschule Dresden,2,,,1952,327,332,,1,0,

,21,0,0,0,0,0,Woodall, D.R.,,,Zeros of chromatic polynomials, in "Combinatorial Surveys: Proc. Sixth British Combinatorial Conference", ed. P. Cameron,,,Academic Press,London,1977,199,223,Emphasises real zeros of chromatic polynomials, including zero-free regions (e.g. [2.5,2.5466]), and multiplicities of integer zeros,1,0,

,21,0,0,0,0,0,Woodall, D.R.,,,A zero-free interval for chromatic polynomials,Discrete Math.,101,,,1992,333,341,For a wide class of near-triangulations, the chromatic polynomial has no zeros between 2 and 2.5,1,0,

s2ab5,26,,,,,,Aberth O.,,,"Precise Numerical Methods using C++",,,Academic Press,,1998,,,,1,,

s2ab6,25,,,,,,Adamson I.T.,,,"Introduction to Field Theory",,,Wiley,New York,1964,,,,1,,

s2ab7,31,,,,,,Agardh C.A.,,,"Sur une méthode élémentaire de résoudre les équations numériques d'un degré quelqonque par la sommation des Series",,,,Carlstad,1847,,,,1,,

s2ab8,2,10,13,17,18,20,Akritas A.G.,,,"Elements of Computer Algebra with Applications",,,John Wiley and Sons,New York,1989,,,,1,,

s2ab11,17,,,,,,Aldaz M. et al,,,Combinatorial Hardness Proofs for Polynomial Evaluation in "Mathematical Foundations of Computer Science 1998" eds L. Brim et al,,,Springer-Verlag,New York,1998,167,175,,1,,

s2ab12,19,,,,,,Al-Kharizmi,,,"Kitab al Mukhtasarfi Hisab al Jabr wa'l Muqabala" ed F.Rosen,,,,London,1830,,,,1,,

s2ab13,19,,,,,,Al-Tusi,,,"Oeuvres mathematiques. Algèbre et géométrie au XIIe siècle vol 2" ed. R. Rashed,,,,Paris,1986,,,,1,,

s2ab22,19,,,,,,Anbouba A.,,,Sharaf al-Din al-Tusi in "Dictionary of Scientific Biography",,,Scribner,New York,1976,514,517,,1,,

s2ab14,1,2,7,,,,Arden B.W.,,,"An Introduction to Digital Computing",,,Addison Wesley,Reading Mass.,1963,,,,1,,

s2ab16,25,,,,,,Artin E.,,,"Foundations of Galois Theory Lectures at New York University",,,New York University,,1938,,,,1,,

s2ab17,22,25,,,,,Artin E.,,,"Modern Higher Algebra: Galois Theory",,,NYU-Courant Inst. of Math,New York,1947,,,,1,,

s2ab18,29,,,,,,Aryabhata,,,"Aryabhatiya of Aryabhata" Trans. K.S. Shukla,,,Indian Nat. Acad. Of Sci.,New Delhi,1976,36,37,,1,,

s2ab19,15,,,,,,Atanassova L.,Kjurkchiev N.,Andreev A.,Two-Sided Multipoints Method for Solution of Non-Linear Equations in "Proc. Internat. Conf. on Numerical Methods and Applications",,,,Sofia,1988,33,37,,1,,

s2bj25,2,,,,,,Bicanic N.,Johnson K.H.,,Who was Raphson?,Internat. J. Numer. Meth. Engrg.,14,,,1979,148,152,,1,,

s2bj1,20,29,,,,,Bach E.,,,Realistic analysis of some randomized algorithms,J. Comput. System Sci.,45,,,1991,30,53,,1,,

s2bj2,25,,,,,,Bachmann P.,,,über Galois' Theorie der algebraischen Gleichungen,Math. Ann.,18,,,1881,449,468,,1,,

,26,0,0,0,0,0,Hitz M.A.,Kaltofen E,Lakshman Y.N.,Efficient Algorithms for Computing the Nearest Polynomial with a Real Root and Related Problems, in "ISSAC '99" ed. S. Dooley,,,Assoc. Comput. Mach.,New York,1999,205,212,Effects of perturbations in coefficients,1,0,

,3,0,0,0,0,0,Bini D.,Fiorentino G.,,Adaptive multiprecision algorithm for univariate polynomial zeros, in "Proc. Of the 1st Internat. MATHEMATICA Sympos.",,,,,1995,53,60,Uses simultaneous root-finding methods,1,0,

,29,0,0,0,0,0,Carruccio E.,,,'Cataldi', in Dictionary of scientific biography (ed. C. Gillispie) vol. 3,,,Charles Scribner's Sons,New York,1971,125,129,Gives algorithm for square roots.,1,0,

,19,0,0,0,0,0,Jerrard G.B.,,,Supplementary remarks on M. Hermite's argument relating to the algebraical resolution of equations of the fifth degree.,Phil. Mag.,23,,,1862,469,470,No note.,1,0,

,19,0,0,0,0,0,Selin H. (ed).,,,Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.,,,Kluwer,Dordrecht,1997,0,0,Low-degree in Mediaeval period in East; Horner's method of solution.,1,0,

s2aj1,13,,,,,,Abaffy J.,Forgo F.,,Globally convergent algorithm for solving nonlinear equations,J. Optim. Theory Appl.,77,,,1993,291,304,,1,,

s2aj3,3,,,,,,Aberth O.,,,Statement of Priority,Math. Comp.,30,,,1976,680,680,,1,,

s2aj4,20,,,,,,Adleman L.M.,Odlyzko A.,,Irreducibility testing and factorization of polynomials,Math. Comp.,41,,,1983,699,709,,1,,

s2aj5,23,,,,,,Adler H.,,,Ein electrisches Gerät zur Auflösung von Polynomgleichungen,Nachrichtentechnik,6 No. 3,,,1956,135,135,,1,,

s2aj6,25,,,,,,Agostini A.,,,Il teorema fondamentale dell'algebra,Period. Mat. Ser. 4,4,,,1924,307,327,,1,,

s2aj7,20,,,,,,Agou S.,,,Factorisation des polynomes a coefficients dans un corps fini,Publ. Dept. Math. Lyons,13 No. 1,,,1976,63,71,,1,,

s2aj10,21,,,,,,Alfaro M.,López G.,Rezola M.L.,Some properties of zeros of Sobolev type polynomials,J. Comput. Appl. Math.,69,,,1996,171,179,,1,,

s2aj11,21,,,,,,Alfaro M.,Marcellán F.,Rezola M.L.,Orthogonal polynomials on Sobolev spaces: Old and new directions,J. Comput. Appl. Math.,48 Nos. 1/2,,,1993,113,131,,1,,

s2aj12,2,12,,,,,Alefeld G.E.,,,Bounding the slope of polynomial operators and some applications,Computing,26,,,1981,227,237,,1,,

s2bb1,2,7,19,29,,,Babinet J.,Housel C.P.,,"Calculs practique appliqués aux sciences d'observation",,,,Paris,1857,,,,1,,

s2bb3,20,29,,,,,Bach E.,,,Realistic analysis of some randomized algorithms in "Proc. Nineteenth Ann. ACM Symp. Theor. Comput.",,,ACM,,1987,453,461,,1,,

s2bb4,20,29,,,,,Bach E.,Shallit J.,,"Algorithmic Number Theory Vol 1. Efficient Algorithms",,,MIT Press,Cambridge Mass.,1996,,,,1,,

s2bb5,29,,,,,,Bannur J.,Varma A.,,The VLSI implementation of a square root algorithm in "Proc. 7th IEEE Symposium on Computer Arithmetic",,,,,1985,159,165,,1,,

s2bb6,25,,,,,,Barbensi G.,,,"P. Ruffini",,,,Modena,1956,,,,1,,

s2bb7,10,11,,,,,Barnett S.,,,"Matrices: Methods and Applications",,,Clarendon Press,,1990,280,321,,1,,

s2bb8,19,,,,,,Becker O.,,,"Der Mathematische Denken der Antike",,,,Gottingen,1966,,,,1,,

s2bb9,10,13,,,,,Beecroft P.,,,"General Method of Finding all the Roots..",,,,Hyde,1854,,,,1,,

s2bb10,4,,,,,,Belanov A.,,,"Solution of Algebraic Equations by Lobachevsky's Method",,,Nauka,Moscow,1989,,,,1,,

s2bb11,31,,,,,,Belardinelli G.,,,Sulle Equazioni Algebriche in "Verhandlungen des Internationalen Mathematiker-Kongress Vol. 2",,,,Zurich,1932,30,30,,1,,

s2bb12,19,25,,,,,Belardinelli G.,,,"Fonctions hypergéométriques de plusieurs variables et résolution analytique des équations algebriques générales",,,Gauthier-Villars,Paris,1960,,,,1,,

s2bb13,19,25,,,,,Bell E.T.,,,"Men of Mathematics",,,,New York,1937,,,,1,,

s2bb14,2,7,,,,,Ben-Israel A.,,,Newton's Method with Modified Functions in "Recent Developements in Optimization Theory and Nonlinear Analysis" Eds. Y. Censor and S. Reich,,,Amer. Math. Soc.,,1997,39,50,,1,,

s2bb15,19,,,,,,Bette,,,"Beitrage zur Auflösung der cubischen und quadratischen Gleichungen",,,,Dresden,1864,,,,1,,

s2bb17,19,,,,,,Betti E.,,,Un teorema sulla risoluzione analitica delle equazione algebriche in "Opere Vol. 1",,,,,,96,101,,1,,

s2bb19,13,,,,,,Bézout E.,,,"Sur la résolution generale des équations de tous degrés",,,,Paris,1765,,,,1,,

s2bb20,19,25,,,,,Bianchi L.,,,"Lezioni sulla teoria dei gruppi di sostituzioni e delle equazioni algebriche secondo Galois",,,,Pisa,1900,,,,1,,

s2bb21,2,13,,,,,Biermann O.,,,"Vorlesungen über mathematisches Näherungsmethodes",,,,Brunswich,1905,,,,1,,

s2bb22,16,30,,,,,Bini D.,,,Divide and conquer techniques for the polynomial root-finding problem in "World Congress of Nonlinear Analysts '92" ed. V. Lakshmikantham,,,Walter de Gruyter,Berlin,1995,3885,3896,,1,,

s2bb23,10,,,,,,Bini D.,Gemignani L.,Pan V.Y.,Improved Parallel Computations with Matrices and Polynomials in "Proc. 18th ICALP LNCS 510" ed. J.L. Albert et al,,,Springer,Berlin,1991,520,531,,1,,

s2bb25,10,18,,,,,Bini D.,Pan V.Y.,,"Polynomial and Matrix Computations Vol. I: Fundamental Algorithms",,,Birkhauser,Boston,1994,,,,1,,

s2bb26,31,,,,,,Birkeland. R.,,,Sur la résolution des équations algébriques in "Cinquième Congrès des Mathématiciens Scandinaves",,,,,1922,171,176,,1,,

s2bb29,19,,,,,,Birkeland R.,,,On the solution of quintic equations in "Proc. International Congress of Mathematicians Vol. 1",,,,Toronto,1924,387,397,,1,,

s2bj3,13,29,,,,,Bailey D.F.,,,A historical survey of solution by functional iteration,Math. Mag.,62,,,1989,155,166,,1,,

s2bj4,17,,,,,,Bakhvalov N.S.,,,On a Stable Evaluation of Polynomials,U.S.S.R. Comp. Math. and Math. Phys.,11 No. 6,,,1971,263,271,,1,,

s2bj5,19,,,,,,Ball R.,,,Note on Biquadratic Equations,Quart. J. Math.,7,,,1865,358,369,,1,,

s2bj6,29,,,,,,Bandyopadhyay S.,Choudhury A.K.,,An iterative cellular array for non-restoring square root extraction,J. of the Institution of Telecommunication Engrs.,19 No. 4,,,1973,169,170,,1,,

s2bj7,21,,,,,,Bartolomeo J.,He M.,,On Faber polynomials generated by an m-star,Math. Comp.,62,,,1994,277,287,,1,,

s2bj8,3,,,,,,Batra P.,,,Improvement of a convergence condition for the Durand-Kerner iteration,J. Comp. Appl. Math.,96,,,1998,117,125,,1,,

s2bj9,17,,,,,,Baur W.,,,Simplified Lower Bounds for Polynomials with Algebraic Coefficients,J. Complexity,13,,,1997,38,41,,1,,

s2bj10,21,,,,,,Bavinck H.,,,On the zeros of certain linear combinations of Chebyshev polynomials,J. Comput. Appl. Math.,65,,,1995,19,26,,1,,

s2bj11,30,,,,,,Bazán F.S.V.,Bezerra L.H.,,On Zero Locations of Predictor Polynomials,Numerical Linear Algebra Appl.,4,,,1997,459,468,,1,,

s2bj12,13,,,,,,Beauzamy B.,,,Products of polynomials and a priori estimates for coefficients in polynomials decompositions: a sharp result,J. Symb. Comput.,13,,,1992,463,472,,1,,

s2bj13,18,20,,,,,Beauzamy B.,Trevisan V.,Wang P.S.,Polynomial Factorization : Sharp Bounds; Efficient Algorithms,J. Symb. Comput.,15,,,1993,393,413,,1,,

s2bj14,31,,,,,,Belardinelli G.,,,Sulla risoluzione delle equazioni algebriche mediante svilluppi in serie,Ann. Mat. Pura Appl. Ser. 3,29,,,1921,251,270,,1,,

s2bj15,19,,,,,,Belardinelli G.,,,L'equazione differenziale risolvente della equazione trinomia,Rend. Circ. Mat. Palermo,46,,,1922,463,472,,1,,

s2bj16,19,,,,,,Belardinelli G.,,,Sur la résolution des équations algébriques,C.R. Acad. Sci. Paris,179,,,1924,432,434,,1,,

s2bj17,31,,,,,,Belardinelli G.,,,Sulla risoluzione della equazioni mediante sviluppi in serie,Rend. Ist. Lombardo,63 Nos. 6/10,,,1930,483,483,,1,,

s2bj18,31,,,,,,Belardinelli G.,,,Rappresentazione delle funzioni algebriche mediante funzioni ipergeometriche,Rend. Ist. Lombardo,67,,,1934,129,138,,1,,

s2bj19,19,,,,,,Belardinelli G.,,,Sulla risoluzione analitica delle equazioni algebriche generali,Rend. Ist. Lombardo,92 No. 1,,,1957,75,75,,1,,

s2bj20,10,13,,,,,Bellavitis G.,,,Appendice alle memorie sulla risoluzione numerica delle equazioni,Memorie del Reale Istituto Veneto di Scienze Lette,,,,1860,177,236,,1,,

s2bb30,2,25,,,,,Blum L. et al,,,"Complexity and Real Computation",,,Springer-Verlag,New York,1997,,,,1,,

s2bb31,6,14,17,,,,Boehm W.,Prautzsch H.,,"Numerical Methods",,,A.K. Peters,,1993,,,,1,,

s2bb32,1,2,7,,,,Borse G.J.,,,"Numerical Methods with MATLAB",,,PWS Publishing Co.,Boston,1997,,,,1,,

s2bb33,19,,,,,,Bortolotti E.,,,"I Contributi del Tartaglia..delle equazioni cubiche",,,,Imola,1926,57,107,,1,,

s2bb34,19,25,28,,,,Borwein P.,Erdélyi T.,,"Polynomials and Polynomial Inequalities",,,Springer-Verlag,,1995,,,,1,,

s2bb35,11,,,,,,Bose N.K.,,,A system-theoretic approach to stability of sets of polynomials in "Linear Algebra and its Role in System Theory: Contemporary Mathematics Vol 47",,,American Math. Soc.,Providence Rhode Isl,1985,25,34,,1,,

s2bb36,25,,,,,,Bourbaki N.,,,"Elements in the History of Mathematics" Trans. J. Meldrum,,,Springer-Verlag,New York,1994,,,,1,,

s2bb37,20,,,,,,Boyd D.W.,,,Large Factors of Small Polynomials in "The Rademacher Legacy to Mathematics" G.E. Andrews et al Eds.,,,Amer. Math. Soc.,,1994,301,308,,1,,

s2bb38,2,7,15,16,,,Brent R.P.,,,The complexity of multiple-precision arithmetic in "Complexity of Computational Problem Solving" Eds. R.S. Anderson and R.P. Brent,,,Univ. of Queensland Press,Brisbane,1975,126,165,,1,,

s2bb39,29,,,,,,Breuer S.,Zwas G.,,"Numerical Mathematics-a Laboratory Approach",,,,Cambridge,1993,,,,1,,

s2bb40,19,,,,,,Brioschi F.,,,intorno ad alcune formule per la risoluzione delle equazioni algebriche in "Opere Vol 1",,,,,,156,156,,1,,

s2bb41,19,,,,,,Brioschi F.,,,Sul metodo di Kronecker per la risoluzione della equazione di 5⁰ grado in "Opere Vol 3",,,,,,177,177,,1,,

s2bb42,19,,,,,,Brioschi F.,,,Osservazioni sulla comunicazione di Maschke riguardante la risoluzione della equazione di sesto grado in "Opere Vol. 4",,,,,,41,41,,1,,

s2bb43,2,7,10,19,,,Briot C.,,,"Leçons d'Algèbre",,,,Paris,1881,,,,1,,

s2bb44,1,3,,,,,Brizard J.,,,"Nouvelle Méthode pour la résolution des équations numériques de tous les degrés",,,Bachelier,Paris,1834,,,,1,,

s2bb45,19,,,,,,Bruins E.M.,,,Numerical solution of equations before and after al-Kashi in "Festschrift für Helmuth Gericke" ed. M. Folkerts and U. Lindgren,,,Franz Steiner Verlag,Stuttgart,1985,105,113,,1,,

s2bb46,10,20,,,,,Buchberger B.,Collins G.E.,Loos R. Eds.,"Computer Algebra: Symbolic and Algebraic Computation",,,Springer-Verlag,,1983,,,,1,,

s2bb47,19,,,,,,Buchner F.,,,"De Algebra Indorum",,,,,1821,,,,1,,

s2bb48,1,2,15,24,,,Burden R.L.,Faires J.D.,,"Numerical Analysis 4/E",,,PWS-Kent,Boston,1989,,,,1,,

s2cj1,19,,,,,,Cagnoli H.,,,Risoluzione numerica delle equazioni di quarto grado per mezzo della Trigonometria,Memorie di Matematica e Fisica della Societa Itali,7,,,1794,28,33,,1,,

s2cj2,2,,,,,,Cahen E.,,,Questions Proposé,Rev. Math. Spec.,8,,,1905,152,152,,1,,

s2cj2,2,,,,,,Cahen E.,,,Questions Proposé,Rev. Math. Spec.,8,,,1905,339,339,,1,,

s2cj3,2,,,,,,Cajori F.,,,Fourier's improvement of the Newton-Raphson method anticipated by Mouraille,Bibliotheca Mathematica (Stockholm) Ser. 3,11,,,1910,132,137,,1,,

s2cj4,10,,,,,,Camargo,Brunetto M.A.O.,Trevisan V.,Isolating complex polynomial roots: An algebraic algorithm using Sturm sequences,Z. Angew. Math. Mech.,76 Supp. 1,,,1996,367,368,,1,,

s2cj5,20,,,,,,Camion P.F.,,,Un algorithme de construction des idempotents primitifs d'idéaux d'algébres sur F_q,C.R. Acad. Sci. Paris,291 Pt. A,,,1980,479,482,,1,,

s2cj6,20,,,,,,Camion P.F.,,,Un algorithme de construction des idempotents primitifs d'idéaux d'algébres sur F_q,Ann. Disc. Math.,12,,,1982,55,63,,1,,

s2cj7,19,,,,,,Cantor M.,,,Petrus Ramus; Michael Stifel; Hieronymus Cardanus,Z. Math. Phys.,2,,,1857,353,376,,1,,

s2cj8,20,,,,,,Carlitz L.,,,Primitive roots in a finite field,Trans. Amer. Math. Soc.,73,,,1952,373,382,,1,,

s2cj9,20,,,,,,Carlitz L.,,,Some problems involving primitive roots in a finite field,Proc. Nat. Acad. Sci. U.S.A.,38,,,1952,314,318,,1,,

s2cj10,20,,,,,,Carlitz L.,,,Some problems involving primitive roots in a finite field,Proc. Nat. Acad. Sci. U.S.A.,38,,,1952,618,618,,1,,

s2cj11,20,,,,,,Carlitz L.,,,An application of a theorem of Stickelberger,Simon Stevin; Groningen,31,,,1956,27,30,,1,,

s2cj12,20,,,,,,Carlitz L.,,,Some problems involving primitive roots in a finite field,Proc. Nat. Acad. Sci. U.S.A.,38,,,1952,314,320,,1,,

s2cj13,20,,,,,,Carlitz L.,,,A special quartic congruence,Math. Scand.,4,,,1956,243,246,,1,,

s2cj14,3,,,,,,Carstensen C.,,,On simultaneous factoring of a polynomial,Internat. J. Comput. Math.,46,,,1992,51,61,,1,,

s2cj15,3,,,,,,Carstensen C.,Petkovic M.S.,Trajovic M.,Weierstrass formula and zero-finding methods,Numer. Math.,69,,,1995,353,372,,1,,

s2cj16,3,,,,,,Carstensen C.,Sakurai T.,,Simultaneous factorization of a polynomial by rational approximation,J. Comput. Appl. Math.,61,,,1995,165,178,,1,,

,13,,,,,,Struik D.J.,,,On Ancient Chinese Mathematics,Math. Teacher,56,,,1963,424,432,Describes early Chinese application of Horner's method,1,0,

s2cj18,13,,,,,,Carvallo E.,,,Théorème fondamental pour la résolution numérique des équations,Nouv. Ann. Math. Ser. 3,10,,,1891,429,433,,1,,

s2cj19,19,,,,,,Cassina U.,,,Su due quesiti proposti da Cardano a Tartaglia,Period. Mat. Ser. 4,9,,,1929,117,117,,1,,

s2cj20,19,,,,,,Cassina U.,,,Su due quesiti proposti da Cardano a Tartaglia,Congress of Mathematicians,6,,,1928,443,448,,1,,

s2cj21,18,,,,,,Catalan,,,Note sur la théorie des équations,C.R. Acad. Sci. Paris,47,,,1858,797,800,,1,,

s2cj22,31,,,,,,Cauchy A.,,,Sur la résolution des équations,C.R. Acad. Sci. Paris,4,,,1837,362,365,,1,,

s2cj23,20,,,,,,Cauchy A.,,,Sur la résolution des équivalences dont les modules se réduisent á des nombres premiers,Exercises Math.,4,,,1829,253,292,,1,,

s2cj24,31,,,,,,Cauchy A.,,,Sur la determination complète de toutes les racines des équations de degré quelconque,C.R. Acad. Sci. Paris,4,,,1837,779,783,,1,,

s2cj25,31,,,,,,Cauchy A.,,,Sur la résolution des équations de degré quelconque,C.R. Acad. Sci. Paris,4,,,1837,805,821,,1,,

s2cj26,31,,,,,,Cauchy A.,,,Note sur la résolution des équations de degré quelconque,C.R. Acad. Sci. Paris,5,,,1837,301,304,,1,,

s2cj27,13,,,,,,Cauchy A.,,,Méthode générale pour la détermination des racines réelles et des équations algébriques ou même transcendentes,C.R. Acad. Sci. Paris,5,,,1837,357,365,,1,,

s2cj28,20,,,,,,Cauchy A.,,,Mémoire sur les racines des équivalences correspondantes á des modules quelconques premiers ou non premiers; et sur les avantages que présente l'emploi de ces racines dans la théorie des nombres,C.R. Acad. Sci. Paris,25,,,1847,37,54,,1,,

s2cj29,13,,,,,,Cauchy A.,,,Sur les quantités géométriques; et sur une methode nouvelle pour la résolution des équations algébriques de degré quelconque,C.R. Acad. Sci. Paris,29,,,1849,250,257,,1,,

s2cj30,31,,,,,,Cauchy A.,,,Sur la résolution des équations et sur le developpement de leurs racines en séries convergent,C.R. Acad. Sci. Paris,38,,,1854,1104,1107,,1,,

s2cj31,19,,,,,,Cayley A.,,,Note on Mr. Cockle's Solution of a Cubic Equation,Cambridge and Dublin Math. J.,6,,,1851,186,186,,1,,

s2cj32,19,,,,,,Cayley A.,,,Fifth Memoir upon Quantics,Philos. Trans. Roy. Soc. London,148,,,1858,429,460,,1,,

s2cj33,19,,,,,,Cayley A.,,,On Tschirnhausen's Transformation,Philos. Trans. Roy. Soc. London,152,,,1862,561,578,,1,,

s2cj34,19,,,,,,Cayley A.,,,Addition to the Memoir on Tschirnhausen's Transformation,Philos. Trans. Roy. Soc. London,156,,,1866,97,11,,1,,

s2cj35,19,,,,,,Cayley A.,,,A solvible case of the quintic equation,Quart. J. Math.,18,,,1882,154,157,,1,,

s2cj36,19,,,,,,Cayley A.,,,On the Jacobian sextic equation,Quart. J. Math.,18,,,1882,52,65,,1,,

s2cj57,19,,,,,,Clebsch A.,,,Ueber die Anwendung der quadratischen Substitution auf die Gleichungen 5^ten Grades und die geometrische Theorie des ebenen Fünfseits,Math. Ann.,4,,,1871,284,345,,1,,

s2cj58,19,,,,,,Coble A.,,,An application of the form problems associated with certain Cremona groups to the solution of equations of higher degree,Trans. Amer. Math. Soc.,9,,,1908,396,424,,1,,

s2cj59,19,,,,,,Coble A.,,,The Reduction of the sextic equation to the Valentiner Form Problem,Math. Ann.,70,,,1911,337,350,,1,,

s2cj60,19,,,,,,Coble A.,,,An application of Moore's cross ratio group to the solution of the sextic equation,Trans. Amer. Math. Soc.,12,,,1911,311,325,,1,,

s2cj61,19,,,,,,Coble A.,,,The equation of the eighth degree,Bull. Amer. Math. Soc.,30,,,1924,301,313,,1,,

s2cj62,19,,,,,,Cockle J.,,,New Solution of a Cubic Equation,Cambridge Math. J.,2,,,1841,248,249,,1,,

s2cj63,19,,,,,,Cockle J.,,,Solution of an equation,Phil. Mag. Ser. 3,22,,,1843,502,503,,1,,

s2cj64,19,,,,,,Cockle J.,,,On a certain equation of the fifth degree,Mechanics Magazine,45,,,1846,581,582,,1,,

s2cj65,13,19,,,,,Cockle J.,,,Horae Algebraicae,Mechanics Magazine,47,,,1847,409,410,,1,,

s2cj66,13,19,,,,,Cockle J.,,,Horae Algebraicae,Mechanics Magazine,48,,,1848,181,183,,1,,

s2cj67,19,,,,,,Cockle J.,,,An Account of the Method of Vanishing Groups,Phil. Mag. Ser. 3,32,,,1848,114,119,,1,,

s2cj68,19,,,,,,Cockle J.,,,Cubic Equations,Mechanics Magazine,53,,,1850,124,124,,1,,

s2cj69,19,,,,,,Cockle J.,,,Cubic Equations,Mechanics Magazine,53,,,1850,329,331,,1,,

s2cj70,19,,,,,,Cockle J.,,,On two remarkable Cubics,Mechanics Magazine,53,,,1850,448,449,,1,,

s2cj71,19,,,,,,Cockle J.,,,Analysis of the Theory of Equations II,Phil. Mag. Ser. 3,37,,,1850,493,509,,1,,

s2cj72,19,,,,,,Cockle J.,,,Cubic and Quintic Equations,Mechanics Magazine,55,,,1851,172,173,,1,,

s2cj73,19,,,,,,Cockle J.,,,Resolution of Quintics,Quart. J. Math.,4,,,1861,5,7,,1,,

s2cj74,19,25,,,,,Cockle J.,,,On the Method of Symmetric Products,Phil. Mag. Ser. 4,7,,,1854,130,138,,1,,

s2cj75,19,,,,,,Cockle J.,,,Theory of Equations of the Fifth Degree,Phil. Mag. Ser. 4,18,,,1859,50,54,,1,,

s2cj76,19,,,,,,Cockle J.,,,Observations on the Theory of Equations of the Fifth Degree,Phil. Mag. Ser. 4,19,,,1860,197,203,,1,,

,27,0,0,0,0,0,Wilkins, J.E.,,,The expected value of the number of real zeros of a random sum of Legendre polynomials.,Proc. Amer. Math. Soc.,125,,,1997,1531,1536,The expected number is n/ $\sqrt{3}$ +o(n^δ for any δ > 0.,1,0,

,20,0,0,0,0,0,Hurwitz, A.,,,Über höhere Kongruenzen,Arch. Math. Phys. (Ser. 3),5,,,1903,17,27,Considers a₁x^p-2+a₂x^p-3+…+a_p-1 ≡ 0 (mod p).,1,0,

,20,0,0,0,0,0,Kühne, H.,,,Bemurkungen zu der Abhandlung der herrn Hurwitz: Über höhere Kongruenzen.,Arch. Math. Phys. (Ser. 3),6,,,1904,174,0,see note on article by Hurwitz.,1,0,

,20,29,0,0,0,0,Mignosi, G.,,,La convergenza in un campo di integrita finito e la risoluzione apiristica dell congrunze binomie.,Rend. Circ. Mat. Palermo,50,,,1926,245,253,Considers e.g. x^{2^r}≡ a (mod 2^α),1,0,

,29,0,0,0,0,0,Knill, R.J.,,,A modified Babylonian algorithm.,Amer. Math. Monthly,99,,,1992,734,737,Algorithm for sqrt(x); z₁=1;a₁ = (x+1)/(x-1), z_k+1=z_k(1+1/a_k),a_k+1 = 2a_k²-1; then z_k → $\sqrt{x}$ from below.,1,0,

,29,0,0,0,0,0,Deslauriers, G.,Dubuc, S.,,Le calcul de la racine cubique selon Héron.,Elem. Math.,51,,,1996,28,34,If a and b are integers whose cubes enclose N, d₁ = N-a³, d₂ = b³-N, Heron takes a + bd₁(b-a)/(bd₁+ ad₂). We give error bounds for this and related formulas.,1,0,

,18,20,0,0,0,0,Boyd, D.W.,,,Speculations concerning the range of Mahler's measure,Canad. Math. Bull.,24,,,1981,453,469,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,18,20,0,0,0,0,Mossinghoff, M.J.,,,Polynomials with small Mahler measure.,Math. Comp.,67,,,1998,1697,1705,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,18,20,0,0,0,0,Rausch, U.,,,On a theorem of Dobrowolski about conjugate numbers.,Colloq. Math.,50,,,1985,137,142,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,20,0,0,0,0,0,Blake, I.F.,Mullin, R.C.,,The Mathematical Theory of Coding.,,,Academic Press,New York,1975,0,0,Section on polynomials over finite fields.,1,0,

,20,0,0,0,0,0,Pless, V.,,,Introduction to the Theory of Error-Correcting Codes.,,,Wiley-Interscience,New York,1982,0,0,Considers factors of xⁿ-1 over finite field.,1,0,

,20,0,0,0,0,0,Tonelli, A.,,,Bemurkung über die Auflösung quadratischer Congruenzen.,Nachr. Akad. Wiss. Gottingen,,,,1891,344,346,Solves xⁿ = c(mod p).,1,0,

,27,0,0,0,0,0,Mallows, C.L.,Schilling, K.,,Random Polynomials with Real Roots.,Amer. Math. Monthly,106,,,1999,477,0,Fix ε > 0 and n ≥ 1, then a polynomial of degree n with random coefficients can be found which has n distinct real roots with probablity ≥ 1-ε,1,0,

,15,0,0,0,0,0,Kalantari, B,,,On the order of convergence of a determinantal family of root-finding methods.,BIT,39,,,1999,96,109,For a family B_m^k of iteration functions for roots, we show that for a fixed m, as k incrreases, the order decreases from m to the positive root of t^k-Σ₀^k-1t^j. Also for fixed k, the order increases with m.,1,0,

,20,29,0,0,0,0,Mathews, G.B.,,,Theory of Numbers,,,Chelsea,New York,1960,0,0,Treats congruences such as x² ≡ a (mod m).,1,0,

,1,2,14,15,0,0,Pozrikidis, C.,,,Numerical Computation in Science and Engineering,,,Oxford,,1998,0,0,Treats bisection, Bairstow and Newton's methods, Laguerre's method.,1,0,

,29,0,0,0,0,0,McBride, A.,,,Remarks on Pell's equation and square root algorithms,Math. Gaz.,83,,,1999,47,52,Newton's method for square roots is related to Pell's equation:- find positive integers u,v so that u²-av² = ± 1 ( a positive integer).,1,0,

,17,0,0,0,0,0,Revah, I.,,,On the number of Multiplications/Divisions Evaluating a Polynomial with Auxiliary Functions.,SIAM J. Comput.,4,,,1975,381,392,Shows that for n < 9, minimum number of mults/divides to evaluate a polynomial is (n+2)/2, while for n ≥ 9 it is almost always (n+1)/2.,1,0,

,17,0,0,0,0,0,Rabin, M.O.,Winograd, S.,,Fast Evaluation of Polynomials by Rational Preparation,Comm. Pure Appl. Math.,25,,,1972,433,458,Treats Pre-conditioning of polynomials by addition,subtraction and multiplication only. Gives an algorithm of order n/2 + O(log n) multiplies and n+o(n) adds. Also considers case where division allowed.,1,0,

,20,0,0,0,0,0,Skolem. T.,,,On a certain connection between the discriminant of a polynomial and the number of its irreducible factors mod p.,Norsk Mat. Tidskr.,34,,,1952,81,85,,1,0,

,25,0,0,0,0,0,Collins, E.,,,Neuer Beweis der Zerlegbarkeit ganzer Functionen in reelle Factoren vom ersten oder zweiten Grade.,J. Reine Angew. Math.,18,,,1838,119,126,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Liouville, J.,,,Sur le principe fondamental de la théorie des équations algébriques.,J. Math. Pure Appl.,4,,,1839,501,508,Treats existence of roots,1,0,

,25,0,0,0,0,0,Deahna, F.,,,Neuer Beweis für die Auflösbarkeit der algebraischen Gleichungen durch reelle oder imaginäre Werthe der Unbekannten.,J. Reine Angew. Math.,20,,,1840,337,339,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Stern,,,Elementarer Beweis eines Fundamentalsatzes aus der Theorie der Gleichungen.,J. Reine Angew. Math.,23,,,1842,370,371,Treats fundamental theorem of algebra.,1,0,

,25,0,0,0,0,0,Moret,,,Beweis der Satzes, dass jede algebraische ganze Function von einer Veränderlichen in Factoren vom ersten Grade aufgelöset werden kann.,J. Reine Angew. Math.,29,,,1845,97,102,Treats existence,1,0,

,25,0,0,0,0,0,Sussman, J.,,,Vereinfachung des Beweises von Cauchy, dass jede Gleichung n^ten Grades wenigstens eine Wurzel hat.,J. Reine Angew. Math.,44,,,1852,57,59,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Foscolo, G.,,,Sulla necessaria esistenza di una radice reale o imaginaria in ogni equazione algebrica.,Giorn. Mat.,2,,,1864,13,16,Treats existence.,1,0,

,25,0,0,0,0,0,Transon, A.,,,Démonstration de deux théorèmes d'algèbre.,Nouv. Ann. Math. (Ser.2),7,,,1868,97,110,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Clifford, W.K.,,,Proof that every rational equation has a root.,Proc. Cambridge Phil. Soc.,2,,,1870,156,157,Dividing an even degree polynomial by a quadratic,and eliminating the constant term of the quadratic, we eventually reach an odd degree polynomial, which is known to have a root.,1,0,

,25,0,0,0,0,0,Kinkelin, H.,,,Neuer Beweis des Vorhandenseins complexer Wurzeln in einer algebraischen Gleichung.,Math. Ann.,1,,,1870,502,506,Treats existence.,1,0,

,25,0,0,0,0,0,Walton, W.,,,A demonstration that every equation has a root.,Quart. J. Math.,11,,,1871,178,182,Uses Leibnitz' theorem.,1,0,

,25,0,0,0,0,0,Walton, W.,,,Démonstration du théorème de Cauchy: Toute équation a une racine.,Nouv. Ann. Math. (Ser. 2),10,,,1871,509,514,Treats existence.,1,0,

,25,0,0,0,0,0,Netto, E.,,,Beweis der Wurzelexistenz algebraischer Gleichungen.,J. Reine Angew. Math.,88,,,1880,16,21,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration du théorème fondamental de la théorie des équations algébriques.,C.R. Acad Sci. Paris,96,,,1882,772,773,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Dutordoir, H.,,,Toute équation algébrique a une racine; démonstration nouvelle.,Ann. Soc. Sci. Bruxelles,7,,,1883,,,Treats existence,1,0,

,25,0,0,0,0,0,Dutordoir, H.,,,Démonstration nouvelle du théorème fondamental de la théorie des équations algébriques.,C.R. Acad. Sci. Paris,97,,,1883,742,744,Treats existence.,1,0,

,25,0,0,0,0,0,Hocks, H.,,,Ueber den Fundamentalsatz der algebraischen Gleichungen.,Z. Math. Phys.,28,,,1883,123,125,Treats fundamental theorem of algebra.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration du théorème de D'Alembert.,Nouv. Ann. Math. (Ser. 3),2,,,1883,241,248,Treats existence.,1,0,

,25,0,0,0,0,0,Fields, J.C.,,,A proof of the theorem: the equation f(z) = 0 has a root where f(z) is any holomorphic function of z.,Amer. J. Math.,8,,,1886,178,179,Proof in terms of minimum distance from origin, if never 0.,1,0,

,25,0,0,0,0,0,Holst, E.,,,Beweis des Satzes dass jede algebraische Gleichung eine Wurzel hat.,Acta. Math.,8,,,1886,155,160,Treats existence of root.,1,0,

,25,0,0,0,0,0,Perott, J.,,,Démonstration du théorème fondamental de l'algèbre.,J. Reine Angew. Math.,88,,,1886,141,146,Treats existence of roots.,1,0,

,25,0,0,0,0,0,von Dalgwick, F.,,,Ueber einen Beweis des Fundamentalsatzes der Algebra.,Z. Math. Phys.,34,,,1889,185,188,Treats existence.,1,0,

,25,0,0,0,0,0,Phragmén, E.,,,Ein elementarer Beweis des Fundamentalsatzes der Algebra.,Svenska Vet. Ofv. Forh.,48,,,1891,113,120,Treats fundamental theorem of algebra.,1,0,

,28,29,0,0,0,0,Brown, J.E.,Xiang G.,,Proof of the Sendov Conjecture for Polynomials of Degree at Most Eight,J. Math. Anal. Appls.,232,,,1999,272,292,If all the zeros of p lie in the unit disk, then it has a critical point within unit distance of each zero. Proved for degree ≤8 and arbitrary degree if at most 8 distinct zeros.,1,0,

,5,0,0,0,0,0,Kravanja, P.,Van Barel, M.,,A Derivative-Free Algorithm for Computing Zeros of Analytic Functions,Computing,63,,,1999,69,91,Gives an algorithm for computing all zeros inside a closed curve, by evaluating integrals along the curve.,1,0,

,2,0,0,0,0,0,Lang, T.,Montuschi, P.,,Very High Radix Square Root with Prescaling and Rounding and a Combined Division/Square Root Unit,IEEE Trans. Comps.,48,,,1999,827,841,Hardware oriented,1,0,

,19,0,0,0,0,0,Beran, L.,,,The complex roots of a quadratic from a circle,Math. Gaz.,83,,,1999,287,291,,1,0,

,25,0,0,0,0,0,Horng, G.,Huang, M.D.,,Solving polynomials by radicals with roots of unity in minimum depth,Math. Comp.,68,,,1999,881,885,Involves Galois groups, splitting fields, etc.,1,0,

,3,0,0,0,0,0,Iliev, A.I.,Semerdzhiev, Kh. I.,,Some Generalizations of the Chebyshev Method for Simultaneous Determination of All Roots of Polynomial Equations,Comput. Math. Math. Phys.,39,,,1999,1384,1391,The multiplicities are assumed known in advance. The methods have cubic order.,1,0,

,29,0,0,0,0,0,Rangacayra, M.,,,The Ganita-Sara-sangraha of Mahaviracarya,,,Madras Govt. Press,,1912,0,0,Considers square & cube root,1,0,

,29,0,0,0,0,0,Karp, A.H.,Markstein, P.,,High Precision Division and Square Root,ACM Trans. Math. Software,23,,,1997,561,589,,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,Studi i richerchi sulla storia della matematica in Italia nei secoli xvi e xvii,,,Zanichelli,Bologna,1828,0,0,History of solution of low-order polynomials,1,0,

,20,0,0,0,0,0,Buchberger B. et al,,,Rechnerorientierte Verfahren,,,B.G. Teubner,Stuttgart,1986,0,0,Section on Berlekamp-Hensel & related algorithms for polynomials over finite fields,1,0,

,21,0,0,0,0,0,Berriochoa, E.,Cachafeiro, A.,,A family of Sobolev orthogonal polynomials on the unit circle,J. Comput. Appl. Math.,105,,,1999,163,173,,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Topics in Random Polynomials,,,Addison-Wesley-Longman,Harlow, U.K.,1998,0,0,Roots of Polynomials with randomly distributed coefficients,1,0,

,3,12,0,0,0,0,Herzberger, J.,,,On the R-Order of Convergence of a Class of Simultaneous Methods for the Inclusion of Polynomial Roots, in "Scientific Computing & Validated Numerics" ed. G. Alefeld,,,Akademie-Verlag,,1996,154,159,Gives interval versions of Weierstrass' & Ehrlich's methods,1,0,

,10,11,0,0,0,0,Saveleva, N.V.,,,Computer Algebra Procedures for Separating the Roots of Algebraic Equations,Comput. Math. Math. Phys.,39,,,1999,1537,1552,Uses determinants involving sums of roots & Bezout matrices,1,0,

,20,0,0,0,0,0,Tchebichef, P.L.,,,Teoria delle Congruenze,,,E. Loescher,Rome,1895,0,0,,1,0,

,10,0,0,0,0,0,Grabiner, D.J.,,,Descartes' Rule of Signs: Another Construction,Amer. Math. Monthly,106,,,1999,854,855,Gives ways of constructing polynomials having maximum number of positive and negative roots allowed by Descartes' Rule,1,0,

,19,31,0,0,0,0,Scheffler, H.,,,Beitrage zur Theorie der Gleichungen,,,Foerster,Leipzig,1891,0,0,,1,0,

,7,0,0,0,0,0,Wu X.,Wu H.,,On a class of quadratic convergence iteration formulae without derivatives,Appl. Math. Comput.,107,,,2000,77,80,Work per iteration = 2 function evaluations and 5 operations,1,0,

,19,13,0,0,0,0,Cossali, D.P.,,,Origine, trasporto in Italia, primi progressi in essa dell'Algebra. Vol II,,,,,0,0,0,Detailed treatment of cubic, quartic,1,0,

,29,0,0,0,0,0,Hayashi, T.,,,The Pancavimsatika in Its Two Recensions: A Study in the Reformation of a Medieval Sanskrit Mathematical Textbook,Indian J. History Sci.,26,,,1991,399,448,Treatment of square roots.,1,0,

,19,0,0,0,0,0,Rosen, F.,,,The algebra of Mohammed ben Musa,,,,London,1831,,,Treats quadratic,1,0,

,2,17,29,0,0,0,Borwein, J.M.,Borwein, P.B.,,On the complexity of familiar functions and numbers,SIAM Rev.,30,4,,,1988,589,601,Considers square roots and evaluation of polynomials by FFT,1,0,

,13,0,0,0,0,0,Wang, Hs'iao-t'ung,,,Arithmetic in Nine Sections,,,,,650,0,0,,1,0,

,13,0,0,0,0,0,Hsia Luan-hsiang,,,Shao-kuang Chui-t'sang,,,,,1850,0,0,,1,0,

,19,0,0,0,0,0,Ting Ch'u-chung,,,Pai-fu-t'ang,,,,,1876,0,0,Deals with square roots,1,0,

,21,0,0,0,0,0,He, M.,,,Numerical results on the zeros of Faber polynomials for m-fold symmetric domains, in "Exploiting symmetry in applied and numerical analysis", ed. E.L. Allgower et al,,,American Math. Soc.,,1994,229,240,,1,0,

,25,0,0,0,0,0,Galois, E,,,Oevres V-X,,,,Paris,1897,1,61,Solutions by radicals,1,0,

,1,0,0,0,0,0,Xavier, C.,Iyengar, S.S.,,Introduction to Parallel Algorithms,,,Wiley,,1998,0,0,Describes a parallel version of the Bisection method,1,0,

,2,17,0,0,0,0,Flanders, H.,,,Scientific Pascal 2/E,,,Springer-Verlag,New York,1996,0,0,Gives Pascal programs for Newton's method and evaluation of polynomials,1,0,

,1,2,0,0,0,0,Ortega, James M,Grimshaw,,An Introduction to C++ and Numerical Methods,,,Oxford University Press,,1998,0,0,Describes Bisection, Newton and gives a C++ program combining the two.,1,0,

,19,0,0,0,0,0,Palter, R.M.,,,Towards Modern Science Vol. 1,,I,,New York,1962,0,0,Early quadratics in Egypt,1,0,

,13,0,0,0,0,0,Safiev, R.A,,,On a modification of the method of tangent hyperbolas (Russian),Dokl. Akad Nauk Azerbaidzan,19,,,1963,3,8,,1,0,

,29,0,0,0,0,0,L'Huillier, H.,,,Concerning the method employed by Nicolas Chuquet for the extraction of cube roots. In "Mathematics from Manuscript to Print 1300-1600", C.Hay (ed),,,Clarendon press,Oxford,1988,89,95,Number split into slices of 3 digits, starting from right. Find integer cube root of group on left, and subtract its cube from left-most group. And so on.,1,0,

,27,0,0,0,0,0,Renganathan, N.,Sambandham, M.,,On the lower bounds of the number of real roots of a random algebraic equation.,Indian J. Pure Appl. Math,13,,,1982,148,157,Estimates stated bound when coefficients are dependent variables with mean zero and an exponential joint density function.,1,0,

,20,0,0,0,0,0,Mines, R.,Richman, F.,,Separability and factoring polynomials,Rocky Mountain J. Math.,12,,,1982,91,102,Factoring over finite fields,1,0,

,3,12,0,0,0,0,Atanassova, L.,Herzberger, J.,,A general approach to a class of single-step methods for the simultaneous inclusion of polynomial zeros in "Validation Numerics: Theory & Appls." ed R. Albrecht et al.,,,Springer-Verlag,,1993,11,19,Uses interval methods,1,0,

,17,0,0,0,0,0,Blum, L.,Shub, M.,,Evaluating rational functions: Infinite precision is finite cost and tractable on average,SIAM J. Comput.,15,,,1986,384,398,Considers loss of precision in evaluating a rational function: the average loss is small.,1,0,

,17,29,0,0,0,0,Tienari, M.,,,On some topological properties of numerical algorithms,BIT,12,,,1972,430,433,Considers errors in arithmetic, including evaluating a polynomial, & taking a square root.,1,0,

,2,0,0,0,0,0,McMullen, C.,,,Braiding of the attractor and the failure of iterative algorithms.,Invent. Math.,91,,,1988,259,272,Gives a generally convergent algorithm for cubics, but shows such does not exist for degree>=4,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,Span of linear combinations of derivatives of polynomials.,Duke Math. J.,34,,,1967,123,130,,1,0,

,29,0,0,0,0,0,Muller, C.,,,Die Mathematik der Sulvasutra,Abh. Math. Sem. Hamburg Univ.,7,,,1930,173,204,Gives ancient Indian formula for $\sqrt{2}$ ,1,0,

,29,0,0,0,0,0,Ramanujacharia, N.,Kaye, G.R.,,The Trisatika of Sridharacarya,Bibl. Math. Ser. 3,13,,,1913,203,217,Covers ancient Indian approximation to square-roots,1,0,

,28,0,0,0,0,0,Sasaki T.,,,A theorem for separating close roots of a polynomial and its derivatives.,ACM SIGSAM Bull.,38-3,,,2004,85,92,Seperates close roots (a cluster) from the others.,1,0,

,30,0,0,0,0,0,Niu X.-M.,Sakurai T.,,A method for finding the zeros of polynomials using a companion matrix,Japan J. Ind. Appl. Math.,20,,,2003,239,256,Finds multipule roots by matrix method.,1,0,

,27,0,0,0,0,0,Samal, G.,,,Number of real zeros of a random algebraic polynomial.,Indian J. Math.,20,,,1978,225,232,If coefficients are independent random variables with expectation 0, 3rd moment finite and not 0, then number of real roots > ε_nlog n, and ε_n is a sequence tending to 0 and ε_nlog n → ∞,1,0,

,27,0,0,0,0,0,Sambandham, M.,,,On the upper bound of the number of real roots of a random algebraic equation,J. Indian Math. Soc.,42,,,1978,15,26,If coefficients are dependent with normal distribution, the equations have at most α(log log n)² log n roots.,1,0,

,29,0,0,0,0,0,Michel, P.H.,,,De Pythagore à Euclid. Contribution à l'histoire des mathématiques préeuclidiennes.,,,,Paris,1950,0,0,Treats $\sqrt{2}$ ,1,0,

,21,0,0,0,0,0,Nicolas, J.L.,Schinzel, A.,,Localisation des zeros de polynômes intervenant en théorie du signal, in"Cinquante Ans de Polynômes", Ed. M. Langevin and M. Waldschmidt,,,Springer-Verlag,New York,1990,167,179,Considers zeros of f(z) = zⁿ⁺¹-(n+1)z+n, and another similar special polynomial.,1,0,

,21,0,0,0,0,0,Nulton, J.D.,Stolarsky, K.B.,,Zeros of certain trinomials,C.R. Math. Rep. Acad. Sci. Cananda,6,,,1984,243,248,If λ fixed, between 0 and 1, and large, then P_n(z) = λzⁿ+1-λ-(λz+1-λ)ⁿ has a zero inside unit circle iff λ is not = reciprocal of a positive integer.,1,0,

,20,0,0,0,0,0,Seelhoff, P.,,,Auflösung der Congruenz x² ≡ r(mod N),Z. Math. Phys.,31,,,1886,378,380,,1,0,

,20,0,0,0,0,0,Wertheim,,,Elemente der Zahlentheorie,,,,,1887,182,183,Also see pp 207-217. Presents theory of x² ≡ a(mod m),1,0,

,19,25,0,0,0,0,Mourey, C.V.,,,La vrai théorie des quantités négatives et des quantités prétendues imaginaires,,,Mallet-Bachelier,Paris,1861,0,0,Deals with roots of cubic, and existence of a root for any equation.,1,0,

,19,0,0,0,0,0,Bertrand, J.,,,"Traité élémentaire d'Algèbre",,,Hachette,Paris,1851,0,0,Treats quadratic equations in usual manner.,1,0,

,2,10,0,0,0,0,Haase, G.,Herzberger, J.,,Schranken für die positive Wurzel von Polynomen in der Finanzmathematik,Z. Angew.Math. Mech.,78 S,,,1998,931,932,,1,0,

,15,16,0,0,0,0,Hernández, M.A.,Salanova, M.A.,,Indices of convexity and concavity. Application to Halley Method,Appl. Math. Comput.,103,,,1999,27,49,Gives conditions for convergence of Halley's method in terms of logarithmic convexity of f and f'.,1,0,

,2,7,10,19,25,0,von Burg, A.,,,Compendium der höheren Mathematik,,,Wien,,1851,0,0,Early treatment of existence, Newton's method, Sturm Sequences, low degree polynomials.,1,0,

,13,0,0,0,0,0,Vahlen,,,Über reductible Binome,Acta Math.,19,,,1895,195,198,,1,0,

,27,0,0,0,0,0,Cramer, H.,Leadbetter, M.R.,,The moments of the number of crossings of a level by a stationary normal process.,Ann. Math. Statist.,36,,,1965,1656,1663,,1,0,

,17,0,0,0,0,0,Barrio, R.,Sabadell, J.,,A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment,SIAM J. Sci. Comput.,20,,,1999,964,969,A parallel algorithm to evaluate polynomials in Chebyshev form takes ∼ 4[ $\log_{2} p] +$ 4[N/p]-7 steps on p processors.,1,0,

,17,0,0,0,0,0,Reif, J.H.,,,Approximate complex polynomial evaluation in near constatnt work per point.,SIAM J. Comput.,28,,,1999,2059,2089,To evaluate at m ≥ n complex points; let Q(z_j) be an ε-approximation of P(z) and |P| = Σ|coefficients|; k = log(|P|/ε). We evaluate at m ≥ n log n/log²k points in work O(log² logn) per point.,1,0,

,17,0,0,0,0,0,Olver, F.W.J.,,,A new Approach to Error Arithmetic,SIAM J. Numer. Anal.,15,,,1978,368,393,Gives expression for error in evaluating a polynomial.,1,0,

,2,7,16,0,0,0,Argyros, I.K.,Szidarovsky, F.,,The Theory and Application of Iteration Methods,,,CRC Press,,1993,0,0,Treats Secant, Newton, Convergence.,1,0,

,29,0,0,0,0,0,Chambers, L.G.,,,An algorithm for the p'th root,Math. Gaz.,83,,,1999,258,260,Uses $x_{n + 1} = x_{n} \frac{x_{n}^{p} + λa}{λ x_{n}^{p} + a}$ where λ= $\frac{p + 1}{p - 1}$ . The method is 3rd order,1,0,

,2,15,0,0,0,0,Crandall, R.,,,Topics in Advanced Scientific Computation,,,Springer-Verlag,New York,1996,0,0,If f(a) = f''(a)=...= $f^{(m - 1)} (a) = 0 and f' (a) \neq 0,$ then $x_{n + 1} = x_{n} - \frac{f (x_{n}) f' (x_{n})}{{f' (x_{n})}^{2} - f (x_{n}) f'' (x_{n}) / m}$ has order m+1,1,0,

,2,0,0,0,0,0,Cayley, A.,,,On the Newton-Fourier Imaginary Problem,Proc. Cambridge Phil. Soc.,3,,,1880,231,232,Not able to find regions of attraction for Newton's method for cubic equation. Can for quadratic.,1,0,

,18,0,0,0,0,0,Ray, G.A.,,,A locally parameterized version of Lehmer's problem, in "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics", ed. W. Gautschi,,,Amer. Math. Soc.,,1994,573,576,Considers whether there exist polynomials with integer coefficients such that Mahler's M(p) is close to 1. Here M(p)= | $a_{n} | Π_{i = 1}^{n}$ max{| $r_{i} |$ ,1}. Solves the problem in some cases,1,0,

,11,0,0,0,0,0,Gleyse, B.,Moflik, M.,,The Exact Computation of the Number of Zeros of a Real Polynomial in the Open unit Disk: An Algebraic Approach,Comput. Math. Appl.,39(1),,,2000,209,214,Answer in terms of Variations in sign of minors of a matrix similar to the Schur-Cohn matrix.,1,0,

,15,0,0,0,0,0,Drakopoulos, V.,,,On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials.,Comput. And Graphics,22,,,1998,629,634,Schröder iterations applied to a cubic have fixed points which satisfy equations of order > 3. We detect points or cycles not corresponding to desired roots.,1,0,

,29,0,0,0,0,0,Datta, B.,Singh, A.N.,,Approximate Values of Surds in Hindu Mathematics,Indian J. History Sci.,28,,,1993,265,275,Gives series for $\sqrt{2}$ , correct to 5D. Also mentions the Bakhshali formula for general square root, among others.,1,0,

,21,0,0,0,0,0,Rovder, J.,,,Zeros of the polynomial solutions of the differential equation xy''+(β₀+ β₁x+ β₂x²)y'+(γ-nβ₂x)y = 0,Matematicki Casopis,24,,,1974,15,20,,1,0,

,17,0,0,0,0,0,Pan, V.Y.,Reif, J.H.,Tate, S.R.,The Power of Combining the Techniques of Algebraic and Numerical Computing: Improved Approximate Multipoint Polynomial Evaluation..in "Proc. 32nd IEEE Symp. Founds. Comp. Sci.",,,IEEE,Pittsburgh,1992,703,713,Developes a multipoint algorithm for evaluation of a polynomial of degree n at m+1 points with error bound 2^-uΣ |p_I| of order m log² u +n min{u,log n}. Parallelization is easy.,1,0,

,29,0,0,0,0,0,Hooper, A.,,,Makers of Mathematics,,,,New York,1948,0,0,Gives Pythagorean method for $\sqrt{2}$ ,1,0,

,20,0,0,0,0,0,Allenby, R.B.J.T.,Redfern, E.J.,,Introduction to number theory with computing,,,Edward Arnold,,1989,0,0,Considers congruences of high order , I.e. find integer u such that f(u) = 0 (mod m),1,0,

,2,0,0,0,0,0,Argyropoulos, N.,Böhm, A.,Drakopoulos, V.,Julia and Mandelbrot-like sets for higher order König rational iteration functions, in "Fractal Frontiers", M.M. Novak and T.G. Dewey (Eds),,,World Scientific,Singapore,1997,169,178,,1,0,

,29,0,0,0,0,0,Channabasappa, M.N.,,,On the Square-Root Formula in the Bakhshali Manuscript,Indian J. History Sci.,11,,,1976,112,124,Gives $\sqrt{Q}$ = $\sqrt{A^{2} + b}$ = A+ $\frac{b}{2 A}$ - $\frac{({\frac{b}{2 A})}^{2}}{2 (A + \frac{b}{2 A})}$ .,1,0,

,19,29,0,0,0,0,Srinivasiengar, C.N.,,,The History of Ancient Indian Mathematics,,,World Press,Calcutta,1967,0,0,Treats square & cube roots, quadratics, some cubics.,1,0,

,19,,0,0,0,0,Gupta, R.C.,,,Centenary of Bakhshali's Manuscript Discovery,Ganita Bharati,3,,,1981,103,105,The manuscript has early Indian Mathematics, e.g. quadratics,1,0,

,19,0,0,0,0,0,Shao, S.P.,Shao, L.P.,,Mathematics for Management and Finance, 6th ed.,,,South-Western Publ. Comp.,Cincinatti,1990,0,0,Covers Quadratics,1,0,

,5,25,0,0,0,0,Sturm, C.,,,D'un Théorème de M. Cauchy, relatif aux racines imaginaires des Equations,J. Math. Pures Appl.,1,,,1836,278,289,Tests whether a closed contour contains a zero of a polynomial. Proves existence of root.,1,0,

,19,0,0,0,0,0,Feldman, Richard Jr.,,,The Cardano-Tartaglia Dispute,Mathematics Teacher,54,,,1961,160,163,Historical only. (No formulas),1,0,

,190,0,0,0,0,0,Grant, E. ed.,,,A Source Book in Medieval Science,,,Harvard Univ. Press,Cambridge, Mass,1974,0,0,Gives original articles by Al-Kharizmi & others on quadratics,1,0,

,29,0,0,0,0,0,Shukla, K.S.,Sarma, K.V.,,Aryabhatiya of Aryabhata,I,,Ind. Nat. Acad. Sci.,New Delhi,1976,0,0,Gives method for square and cube roots of large integers.,1,0,

,20,0,0,0,0,0,Apostol, T.M.,,,Introduction to Analytic Number Theory,,,Springer,,1979,0,0,Considers polynomial congruences,1,0,

,17,0,0,0,0,0,von zur Gathen, J.,Strassen, V.,,Some polynomials that are hard to compute,Theoret. Comput. Sci.,11,,,1980,331,336,,1,0,

,19,0,0,0,0,0,Morley, H.,,,Jerome Cardan. The Life of Girolamo Cardano, of Milan, Physician,,,Chapman & Hall,London,1854,0,0,Reprinted Xerox University Microfilms, (1976). Treats solution of cubic historically; dispute with Tartaglia etc.,1,0,

,13,0,0,0,0,0,Delagny,,,Nouveaux Elémens d'Arithmetique et d'Algèbre,,,,Paris,1697,0,0,,1,0,

,13,0,0,0,0,0,Hume, J.,,,Algèbre de Viete, d'une méthode nouvelle, claire et facile,,,,Paris,1636,0,0,,1,0,

,13,0,0,0,0,0,Hérigone, P.,,,Cursus Mathematicus II,,,,Paris,1642,0,0,,1,0,

,13,0,0,0,0,0,Rolle, M.,,,Traité d'Algèbre ,,,,,,1690,0,0,,1,0,

,19,29,0,0,0,0,Simon, M.,,,Geschichte der Mathematik im Altertum,,,,Berlin,1909,0,0,Considers quadratics, roots,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Location of the Zeros of Polynomials satisfying three-term recurrence relations with complex coefficients,Integral Trans. & Special Functions,2,,,1994,267,278,It shows that this new method of optimization is sharp in the following sense: it leads to the exact interval where all zeros of classical orthogonal polynomials are located.,1,0,

,3,16,0,0,0,0,Milovanovic, G.V.,Petkovic, M.S.,,Computational Efficiency of the Simultaneous Methods for Finding Polynomial Zeros; Estimation of Efficiency, in "Numerical Methods & Approx. Theory, Novi Sad, 1985",,,,,1985,83,94,A Measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the so-called coefficient of effficiency, is considered in the paper.,1,0,

,16,0,0,0,0,0,Herzberger, J.,,,Wissenschaftliches Rechnen. Chap 7,,,Akademie Verlag,,1995,0,0,Considers order of convergence.,1,0,

,5,0,0,0,0,0,Kravanja, P.,Sakurai, T.,Van Barel, M.,On locating clusters of zeros of analytic functions.,BIT,39,,,1999,646,682,Finds all zeros with multiplicities contained within a Jordan curve.,1,0,

,17,0,0,0,0,0,Bauer, W.,Rabin, M.O.,,Linear Disjointness and Algebraic Complexity in "Logic and Algorithmic: an International Symposium held in Honour of E. Specker",,,Enseign. Math.,Geneva,1982,35,46,Considers preprocessing coefficients before evaluation,1,0,

,20,0,0,0,0,0,Stark, H.M.,,,An Introduction to Number Theory,,,MIT Press,Cambridge, Mass.,1979,0,0,Section on polynomial congruences.,1,0,

,17,0,0,0,0,0,Aldaz, M. et al,,,Time-Space Tradeoffs in Algebraic Complexity Theory,J. Complexity,16,,,2000,2,49, $For evaluation of polynomials of degree d we$ show Time x Space ≥ $\frac{d}{8}$ . Hence usually Space ≥.c $\sqrt[4]{d}$ ,1,0,

,1,2,0,0,0,0,Pan, V.Y.,,,Approximating Complex Polynomial Zeros: Modified Weyl's Quadtree Construction and Improved Newton's Iteration,J. Complexity,16,,,2000,213,264,Time of order n²log n log bn to get all roots with error bound 2^-bmax|z_j|,1,0,

,20,0,0,0,0,0,Cipolla, M.,,,Theoria de Congruentias intra Numeros Integro,Revista Math.,8,,,1905,87,117,,1,0,

s2cb4,31,,,,,,Cajori F.,,,"A History of the Arithmetical Methods of Approximation to the Roots of Numerical Equations of one Unknown Quantity",,,Colorado College Publ. Sc,,1910,,,,1,,

s2cb5,2,,,,,,Cajori F.,,,"William Oughtred: a great seventeenth-century teacher of mathematics",,,Open Court,London,1916,,,,1,,

s2cb6,30,,,,,,Cardinal J.P.,,,On two iterative methods for approximating the roots of a polynomial in "Proc. of Workshop on Mathematics of Numerical Analysis" J. Renegar et al Eds.,,,Amer. Math. Soc.,,1995,165,188,,1,,

s2cb7,7,17,19,29,,,Cassina U.,,,"Calcolo Numerico",,,,Bologna,1928,,,,1,,

s2cb8,2,10,19,25,,,Cesàro E.,Kowalewsky G.,,"Elementares Lehrbuch der alg. Analysis; art. 431",,,,,,,,,1,,

s2cb9,2,26,,,,,Chaitin-Chatelin F.,Frayse V.,,"Lectures on Finite Precision Computations",,,Soc. Ind. Appl. Math.,,1996,45,47,,1,,

s2cb10,2,,,,,,Chen T.-C.,,,Iterative zero-finding revisited in "Computational Techniques and Applications: CTAC-89" W.I. Hogarth and B.J. Noye Eds.,,,Hemisphere Publ. Corp.,New York,1990,583,590,,1,,

s2cb11,2,,,,,,Chen T.-C.,,,SCARFS; an efficient polynomial zero-finder in "Proc. Int'l Conf. on APL",,,Toronto,Canada,1993,47,54,,1,,

s2cb12,15,,,,,,Chen T.-C.,,,Convergence in iterative polynomial root-finding in "Proc. Workshop on Numerical Analysis and Applications" eds. L. Vulkov and J. Wasniewski,,,Springer-Verlag,,1997,98,105,,1,,

s2cb13,3,,,,,,Chen T.-C.,Luk W.-S.,,Aberth's method for the parallel iterative finding of polynomial zeros in "APL94 Conference Proceedings",,,Antwerp,Belgium,1994,40,49,,1,,

s2cb14,21,,,,,,Chihara T.S.,,,The three-term recurrence relation and spectral properties of orthogonal polynomials in "Orthogonal Polynomials: Theory and Practise" P. Nevai Ed.,,,Kluwer,Dordrecht,1990,99,114,,1,,

s2cb15,10,20,25,,,,Childs L.,,,"A Concrete Introduction to Higher Algebra",,,Springer-Verlag,New York,1979,,,,1,,

s2cb16,13,,,,,,Ch'in,,,"Chiu-shao; Su-shu Chiu-chang",,,,,1247,,,,1,,

s2cb17,19,,,,,,Chu,,,"Chi-Chieh; Suan-hsiao Chi-ming",,,,,1299,,,,1,,

s2cb18,2,4,6,,,,Chudnovsky D.V.,Chudnovsky G.V.,,Computer algebra in the service of mathematical physics and number theory in "Computers in Mathematics" eds. D.V. Chudnovsky and R.D. Jenks,,,Marcel Dekker,,1990,109,232,,1,,

s2cb19,19,,,,,,Chuzen M.,,,"Kaisho Tempei Sampo",,,,,1765,,,,1,,

s2cb20,1,2,5,14,26,,Cohen A.M. et al,,,"Numerical Analysis",,,John Wiley and Sons,New York,1973,21,45,,1,,

s2cb21,2,20,29,,,,Cohen H.,,,"A Course in Computational Algebraic Number Theory",,,Springer,Berlin,1993,,,,1,,

s2cb22,20,,,,,,Cohen S.,Niederreiter H. Eds.,,"Finite Fields and Applications",,,Cambridge Univ. Press,,1996,73,84,,1,,

s2cb23,20,,,,,,Cohen S.,Niederreiter H. Eds.,,"Finite Fields and Applications",,,Cambridge Univ. Press,,1996,163,180,,1,,

s2cb24,20,,,,,,Cohen S.,Niederreiter H. Eds.,,"Finite Fields and Applications",,,Cambridge Univ. Press,,1996,349,354,,1,,

s2cb25,19,,,,,,Colebrooke H.T. Transl.,,,"Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara",,,John Murray,London,1973,,,,1,,

s2cb26,13,,,,,,Collins,,,"Correspondence of Scientific Men of the 17th Century; Vol 1",,,,Oxford,1841,216,243,,1,,

s2cb27,13,,,,,,Collins,,,"Correspondence of Scientific Men of the 17th Century; Vol 2",,,,Oxford,1841,198,219,,1,,

s2cb28,13,,,,,,Collins,,,"Correspondence of Scientific Men of the 17th Century; Vol 2",,,,Oxford,1841,472,472,,1,,

s2cb29,10,,,,,,Collins G.E.,Johnson J.R.,,Quantifier elimination and the sign variation method for real root isolation in "Proc. ACM SIGSAM 1989 International Symp. on Symbolic and Algebraic Computation",,,Assoc. Comp. Mach.,New York,1989,264,271,,1,,

s2cb30,5,,,,,,Collins G.E.,Krandick W.,,An efficient algorithm for infallible complex root isolation in "Proc. Internat. Symp. on Symbolic and Algebraic Computation" ed. P.S. Wang,,,ACM Press,Baltimore Maryland,1992,189,194,,1,,

s2cb31,2,,,,,,Collins G.E.,Krandick W.,,A Hybrid Method for High Precision Calculation of Polynomial Real Roots in "Proc. Intern. Symposium on Symbolic and Algebraic Computation",,,ACM Press,,1993,47,52,,1,,

s2cb33,19,,,,,,Crelle A.L.,,,"Lehrbuch der Arithmetik and Algebra",,,,Berlin,1825,,,,1,,

s2cb1,19,,,,,,Cagnoli H.,,,"Traité de Trigonométrie",,,,Paris,1786,,,,1,,

s2cb2,19,,,,,,Cajori F.,,,"On the transformation of algebraic equations by E. Bring",,,Colorada College Publ. Se,,1907,64,91,,1,,

s2cb3,2,4,7,10,19,20,Cajori F.,,,"A History of the Arithmetical Methods of Approximation to the Roots of Numerical Equations of one Unknown Quantity",,,Colorado College Publ. Sc,,1910,,,,1,,

s2dj1,20,,,,,,Dalen K.,,,On a theorem of Stickelberger,Math.Scand.,3,,,1955,124,126,,1,,

s2dj2,27,,,,,,Das M.,,,The average number of maxima of a random algebraic curve,Proc. Camb. Phil. Soc.,65,,,1969,741,753,,1,,

s2dj3,27,,,,,,Das M.,,,Real zeros of a class of random algebraic polynomials,J. Indian Math. Soc.,36,,,1972,53,63,,1,,

s2dj4,2,29,,,,,Data B.,,,Narayana's method for finding approximate values of a surd,Bull. Calcutta Math. Soc.,23 No. 4,,,1931,187,194,,1,,

s2dj5,29,,,,,,Datta B.,,,On MÛLA; The Hindu term for ``Root'',Amer. Math. Monthly,34,,,1927,420,423,,1,,

s2dj6,29,,,,,,Datta B.,,,On the origin of the Hindu term for ``Root'',Amer. Math. Monthly,38,,,1931,371,376,,1,,

s2dj7,20,,,,,,Davenport H.,,,On primitive roots in a finite field,Quart. J. Math. Oxford Ser. 1,8,,,1937,308,312,,1,,

s2dj8,20,,,,,,Daykin D.E.,,,The irreducible factors of (cx+d)x^{q^m}-(ax+b) over GF(q),Quart. J. Math. Ser.2,14,,,1963,61,64,,1,,

s2dj9,29,,,,,,Dean K.J.,,,Cellular logical array for extracting square roots,Electron. Lett.,4,,,1968,314,315,,1,,

s2dj30,21,,,,,,Dubeau F.,Savoie J.,,On the Roots of Orthogonal Polynomials and Euler-Frobenius Polynomials,J. Math. Anal. Appl.,196,,,1995,84,98,,1,,

s2dj31,27,,,,,,Dunnage J.E.A.,,,The number of real zeros of a random trigonometric polynomial,Proc. London Math. Soc. Ser. 3,16,,,1966,53,84,,1,,

s2dj32,2,19,,,,,Dunnett R.,,,Newton-Raphson and the Cubic,Math. Gaz,78,,,1994,347,348,,1,,

s2dj33,10,18,,,,,Dupré,,,Sur la résolution des équations numériques,C.R. Acad. Sci. Paris,45,,,1857,585,587,,1,,

s2dj34,13,,,,,,D.V.S.,,,On Horner's Synthetic Division,The Mathematician,1,,,1845,74,76,,1,,

s2db1,2,7,26,,,,Dahlquist G.,Björk A.,,"Numerical Methods",,,Prentice-Hall,New Jersey,1974,,,,1,,

s2db2,7,,,,,,Dantzig T.,,,"The Bequest of the Greeks",,,Scribner's,New York,1955,152,159,,1,,

s2db3,19,29,,,,,Datta B.,Singh A.N.,,"History of Hindu Mathematics",,,Asia Publ. House,Bombay,1935,,,,1,,

s2db4,10,20,,,,,Davenport J.,Gianni P.,Trager B.M.,Scratchpad's view of algebra II: a categorical view of factorization in "Proc. 1991 Internat. Symp. Symbolic and Algebraic Computation" ed S.M. Watt,,,ACM Press,,1991,32,38,,1,,

s2db5,10,,,,,,Davenport J.,Padget J.,,HEUGCD: how elementary upper bounds generate cheaper data in "Proc. EUROCAL 85 Vol. 2; LNCS 204",,,Springer-Verlag,New York,1985,18,28,,1,,

s2db6,10,,,,,,Davenport J.,Padget J.,,On Numbers and Polynomials in "Computers and Computing" eds P. Chenin et al,,,Masson and Wiley,,1985,49,53,,1,,

s2db7,10,20,,,,,Davenport J.H.,Siret Y.,Tournier E.,"Computer Algebra",,,Academic Press,,1988,,,,1,,

s2db8,2,7,10,18,19,25,De Comberousse C.,,,"Cours d'Algèbre Supérieure; Vol. 1/2",,,Gauthier-Villars,Paris,1904,,,,1,,

s2db9,29,,,,,,De Comberousse C.,,,"Cours d'Algèbre Supérieure; Vol. 1/2",,,Gauthier-Villars,Paris,1904,,,,1,,

s2db10,2,4,7,10,13,18,de Montessus R.,d'Adhémar R.,,"Calcul Numérique",,,Doin et Fils,Paris,1911,,,,1,,

s2db11,19,25,,,,,de Montessus R,d'Adhémar R.,,"Calcul Numérique",,,Doin et Fils,Paris,1911,,,,1,,

s2db12,5,,,,,,De Morgan A.,,,"Trigonometry and Double Algebra",,,,London,1849,141,144,,1,,

s2db13,2,13,,,,,De Morgan A.,,,Notices of the Progress of the Problem of Evolution in "Companion to the British Almanac",,,,,1839,34,52,,1,,

s2db14,2,13,,,,,De Morgan A.,,,Involution and Evolution in "Penny Cyclopedia",,,,,1842,7,11,,1,,

s2db15,2,10,19,,,,Dienger J.,,,"Theorie und Auflösung der höheren Gleichungen",,,,Stuttgart,1866,,,,1,,

s2db16,2,12,,,,,Dimitrova N.S.,,,On a Parallel Method for Enclosing Real Roots of Nonlinear Equations in "Advances in Numerical Methods and Applications; Sofia; 1994" ed. I.T. Dimov et al,,,World Scientific,,1994,78,84,,1,,

s2db17,19,,,,,,Diophantus,,,in "Dictionary of Scientific Biography" Ed. C.C. Gillispie,,,Scribner's,New York,1971,110,118,,1,,

s2db18,19,,,,,,Diophantus,,,of Alexandria in "Les six livres arithmetiques" ed. Blanchard,,,,Paris,1959,,,,1,,

s2db20,10,25,,,,,Dörrie H.,,,"One Hundred Great Problems of Elementary Mathematics",,,Dover,New York,1965,,,,1,,

s2db21,2,10,25,,,,Drobisch M.W.,,,"Grundzüge der Lehre von den höheren numerischen Gleichungen",,,,Leipzig,1834,,,,1,,

s2db22,18,,,,,,Dubickas A.,,,An estimation of the difference between two zeros of a polynomial in "New Trends in Probablility and Statistics; Vol. 2" eds. F. Schweiger and E. Manstavicius,,,VSP BV/ Vilnius Universit,,1992,17,21,,1,,

s2db23,25,,,,,,Dummit D.S.,Foote R.M.,,"Abstract Algebra",,,Prentice- Hall,Englewood Cliffs N.J,1991,,,,1,,

s2db24,19,,,,,,Dyksterhuis E.J.,,,"The Life and Work of Simon Stevin",,,Swets and Zeitlinger,Amsterdam,1955,,,,1,,

s2ej1,27,,,,,,Edelman A.,Kostlan E.,,How many zeros of a random polynomial are real?,Bull. Amer. Math. Soc.,32,,,1995,1,37,,1,,

s2ej2,27,,,,,,Edelman A.,Kostlan E.,,erratum,Bull. Amer. Math. Soc.,33,,,1996,325,325,,1,,

s2ej3,30,,,,,,Edelman A.,Murakami H.,,Polynomial roots from companion matrix eigenvalues,Math. Comp.,64,,,1995,763,776,,1,,

s2ej4,10,,,,,,Eggar M.H.,,,On the Discriminant Criterion and a Generalization,Amer. Math. Monthly,103,,,1996,788,792,,1,,

s2ej5,19,,,,,,Eisenstein F.G.M.,,,Allgemeine Auflösung der Gleichungen von den ersten vier Graden,J. Reine Angew. Math.,27,,,1844,81,83,,1,,

s2ej6,19,,,,,,Eisenstein F.G.M.,,,Eigenschaften und Beziehungen der Ausdrücke; welche bei der Auflösung der allgemeinen cubischen Gleichungen erscheinen,J. Reine Angew. Math.,27,,,1844,319,321,,1,,

s2ej7,4,,,,,,Encke,,,Allgemeine Auflösung der numerischen Gleichungen,J. Reine Angew. Math.,22,,,1841,193,248,,1,,

s2ej8,4,,,,,,Encke,,,Résolution Générale des équations Numériques,Nouv. Ann. Math.,13,,,1854,81,81,,1,,

s2ej9,19,,,,,,Eneström G.,,,Hat Tartaglia; seine Lösung der kubischen Gleichung von del Ferro entlehnt,Bibliotheca Mathematica; Stockholm; Ser. 3,7,,,1906,38,43,,1,,

s2ej10,19,,,,,,Eneström G.,,,Hat Tartaglia; seine Lösung der kubischen Gleichung von del Ferro entlehnt,Bibliotheca Mathematica; Stockholm; Ser. 3,7,,,1906,292,293,,1,,

s2ej11,19,,,,,,Eneström G.,,,Hat Tartaglia; seine Lösung der kubischen Gleichung von del Ferro entlehnt,Bibliotheca Mathematica; Stockholm; Ser. 3,7,,,1906,300,307,,1,,

s2ej12,19,,,,,,Eneström G.,,,Untitled,Bibliotheca Mathematica; Stockholm; Ser. 3,8,,,1907,87,87,,1,,

s2ej13,19,,,,,,Eneström G.,,,Untitled,Bibliotheca Mathematica; Stockholm; Ser. 3,9,,,1908,259,259,,1,,

s2ej14,19,,,,,,Eneström G.,,,Rezensionen,Bibliotheca Mathematica; Stockholm; Ser. 3,8,,,1907,417,420,,1,,

s2ej15,15,,,,,,Eneström G.,,,Kleine Mitteilungen,Bibliotheca Mathematica; Stockholm; Ser. 3,11,,,1911,234,237,,1,,

s2ej16,19,,,,,,Eneström G.,,,Untitled,Bibliotheca Mathematica; Stockholm; Ser. 3,13,,,1912,166,167,,1,,

s2ej17,19,,,,,,Enneper A.,,,Notiz über die biquadratische Gleichung,Z. Math. Phys.,18,,,1873,93,96,,1,,

s2ej18,29,,,,,,Ercegovac M.D.,Lang T.,,On-the-fly conversion of redundant into conventional representations,IEEE Trans. Comput.,36,,,1987,895,897,,1,,

s2ej19,29,,,,,,Ercegovac M.D.,Lang T.,,Radix-4 square root without initial PLA,IEEE Trans. Comput.,39,,,1990,1016,1024,,1,,

s2ej20,29,,,,,,Ercegovac M.D.,Lang T.,,Module to perform multiplication; division; and square root in systolic arrays for matrix computation,J. Parallel and Distributed Computing,11,,,1991,212,221,,1,,

s2ej21,21,,,,,,Erdélyi T.,,,Nikolskii-type inequalities for generalized polynomials and zeros of orthogonal polynomials,J. Approx. Theory,67,,,1991,80,92,,1,,

s2ej22,21,,,,,,Erdélyi T.,Nevai P.,,Generalized Jacobi weights; Christoffel functions and zeros of orthogonal polynomials,J. Approx. Theory,69,,,1992,111,132,,1,,

s2ej23,21,,,,,,Erdös P.,Turán P.,,``On interpolation II/III'',Ann. of Math. Ser. II,39,,,1938,703,724,,1,,

s2ej23,21,,,,,,Erdös P.,Turán P.,,``On interpolation II/III',Ann. of Math. Ser. II,41,,,1940,510,555,,1,,

s2ej25,20,29,,,,,Escott E.B.,,,Cubic congruences with three real roots,Ann. of Math. Ser. 2,11,,,1910,86,92,,1,,

s2ej26,10,,,,,,Ettinghaus,,,Die Sätze von Fourier und Sturm zur Theorie der algebraischen Gleichungen,J. Reine Angew. Math.,13,,,1835,119,158,,1,,

s2ej27,29,,,,,,Euler L.,,,De solutione problematum Diophanteorum per numeros integros,Opera Omnia Ser. 1,2,Teubner,Leipzig,1911,6,17,,1,,

s2eb1,7,13,,,,,Egen,,,"Ueber die methoden zahlengleichungen durch naherung aufzuloesen",,,,Elbenfeld,1829,,,,1,,

s2eb2,19,20,25,,,,Ehrlich G.,,,"Fundamental Concepts of Abstract Algebra",,,PWS-Kent Publ. Co.,Boston,1991,,,,1,,

s2eb3,20,29,,,,,Elia M.,,,Some comments on the computation of n'th roots in Z^*_n in "Sequences II: Methods in Communication; Security and Computer Science",,,Springer-Verlag,,1993,379,391,,1,,

s2eb4,10,,,,,,Emiris I.Z.,Galligo A.,Lombardi H.,Numerical Univariate Polynomial GCD in "The Mathematics of Numerical Analysis" Eds. J. Renegar et al,,,Amer. Math. Soc.,,1995,323,343,,1,,

s2eb5,10,20,,,,,Encarnacion M.J.,,,On a Modular Algorithm for Computing GCDs of Polynomials Over Algebraic Number Fields in "Proc. Intern. Symp. on Symbolic and Algebraic Computation",,,Ass. Computing Mach.,,1994,58,65,,1,,

s2eb6,20,,,,,,Engelman C.,,,The Lecacy of Mathlab 68 in "Proc. Second Symp. on Symbolic and Algebraic Manipulation",,,Ass. Comp. Mach.,,1971,29,41,,1,,

s2eb7,21,,,,,,Engels H.,,,"Numerical Quadrature and Cubature",,,Academic Press,London,1980,226,237,,1,,

s2eb8,29,,,,,,Ercegovac M.D.,,,An on-line square rooting algorithm in "Proc. 4th IEEE Symp. Computer Arithmetic",,,Santa Monica,Calif.,1978,183,189,,1,,

s2eb9,29,,,,,,Ercegovac M.D.,Lang T.,,On-line computation of rotation factors in "Proc. 8th IEEE Symp. Computer Arithmetic",,,Como,Italy,1987,196,203,,1,,

s2eb10,29,,,,,,Ercegovac M.D.,Lang T.,,Implementation of Module combining Multiplication; Division; and Square Root in "Proc. IEEE Intl. Symp. on Circuits and Systems",,,,,1989,150,153,,1,,

s2eb11,29,,,,,,Ercegovac M.D.,Lang T.,,On-the-fly rounding for division and square root in "Proc. 9th IEEE Symposium on Computer Arithmetic",,,,,1989,169,173,,1,,

s2eb12,29,,,,,,Ercegovac M.D.,Lang T.,,Radix-4 square root without initial PLA in "Proc. 9th IEEE Symposium on Computer Arithmetic",,,,,1989,162,168,,1,,

s2eb13,29,,,,,,Ercegovac M.D.,Lang T.,,"Division and Square Root: Digit Recurrence Algorithms and Implementations",,,Kluwer,Norwell MA,1994,,,,1,,

s2eb15,19,29,,,,,Erler M.,,,"Zur Geschichte der deutschen Algebra im 15. Jahrhundert",,,,Zwickau,1887,,,,1,,

s2eb16,17,,,,,,Estrin G.,,,Organization of Computer Systems-the Fixed Plus Variable Structure Computer in "Proc. Western Joint Computer Conf.",,,,,1960,33,40,,1,,

s2eb17,1,2,7,,,,Etter D.M.,,,"Fortran 77 with Numerical Methods for Engineers and Scientists",,,Benjamin/Cummins,,1992,,,,1,,

s2eb18,20,,,,,,Evdokimov S.A.,,,Factorization of polynomials over finite fields in subexponential time under GRH in "Algorithmic Number Theory; First International Symposium; ANTS1" Eds. L.M. Adleman and M.D. Huang,,,Springer- Verlag,,1994,209,212,,1,,

s2eb19,19,,,,,,Euler L.,,,"Elements of Algebra" trans. J. Hewlett,,,Springer-Verlag,,1984,,,,1,,

s2eb20,6,14,,,,,Evans G.A.,,,"Practical Numerical Analysis",,,Wiley,,1995,,,,1,,

s2eb21,10,13,19,,,,Eyteleween D.J.U.,,,"Die Grundlehren der höheren Analysis",,,,Berlin,1824,,,,1,,

s2fb6,20,,,,,,Fleischmann P.,Roelse P.,,Comparative implementations of Berlekamp's and Niederreiter's polynomial factorization algorithms in "Finite Fields and Applications" S. Cohen and H. Niederreiter Eds.,,,Cambridge Univ. Press,,1996,73,84,,1,,

s2fb7,3,13,16,,,,Fleury E.,Fraigniaud P.,,Fine and coarse grained parallel implementations of polynomial root finding algorithms in "World Congress of Nonlinear Analysts '92" ed. V. Lakshmikantham,,,Walter de Gruyter,Berlin,1995,3871,3884,,1,,

s2fb8,17,29,,,,,Flores I.,,,"The Logic of Computer Arithmetic",,,Prentice-Hall,,1963,,,,1,,

s2fb9,1,2,7,17,24,26,Flowers B.H.,,,"An Introduction to Numerical Methods in C++",,,Clarendon Press,,1995,,,,1,,

s2fb10,2,4,10,18,,,Focke M.F.,,,"De Aequationibus Numericis Superioris Ordinis",,,Monasterii,,1856,,,,1,,

s2fb11,2,13,,,,,Fourier J.B.J.,,,"Analyse des équations determineés",,,,Paris,1831,,,,1,,

s2fb12,3,,,,,,Fraigniaud P.,Gastaldo M.,,Influence of the SIMD programming mode on sorting and extracting the roots of a polynomial in "Proc. of the ISMM Fifth Internat. Conf. on Parallel and Distributed Computing and Systems" Ed. R. Melhem,,,International Soc. for Mi,,1993,230,237,Published by International Society for Mini- and Micro-Computers,1,,

s2fb14,25,,,,,,Fraleigh J.B.,,,"A First Course in Abstract Algebra",,,Addison-Wesley,Reading Mass.,1982,,,,1,,

s2fb15,2,6,10,19,25,,Francoer L.,,,"Cours Complet de Mathématiques Pures",,,Bachelier,Paris,1837,,,,1,,

s2fb16,2,7,15,17,29,,Fröberg C.E.,,,"Numerical Mathematics: Theory and Computer Applications",,,The Benjamin/Cummings Pub,,1985,,,,1,,

s2fb17,21,,,,,,Funaro D.,,,"Polynomial Approximation of Differential Equations: Lecture Notes in Physics ",,,SIAM,Philadelphia,1977,,,,1,,

s2fb18,30,,,,,,Fürstenau,,,"Darstellung der reellen Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten",,,,Marburg,1860,,,,1,,

s2gj1,25,,,,,,Galois E.,,,Recherches sur la théorie des permutations et des équations algébriques; ed. J. Tannery,Bull. Sci. Math. Ser. 2,31,,,1907,275,308,,1,,

s2gj2,13,,,,,,Gandz S.,,,On the origin of the term ``root'',Amer. Math. Monthly,35,,,1928,67,75,,1,,

s2gj3,19,,,,,,Gandz S.,,,Conflicting Interpretations of Babylonian Mathematics,Isis,31,,,1940,405,425,,1,,

s2gj4,17,,,,,,Ganz J.,,,Evaluation of polynomials using the structure of the coefficients,SIAM J. Comput.,24,,,1995,473,483,,1,,

s2gj5,32,,,,,,Gao T.,Wang Z.,,On the complexity of a PL homotopy algorithm for zeros of polynomials,Acta Math. Appl. Sinica,9,,,1993,135,142,,1,,

s2gj6,21,,,,,,Gatteschi L.,,,New error bounds for asymptotic approximations of Jacobi polynomials and their zeros,Rend. Mat. Ser. 7,14,,,1994,177,198,,1,,

s2gj7,13,,,,,,Gauss C.F.,,,Beweis eines algebraischen Lehrsatz,J. Reine Angew. Math.,3,,,1828,1,4,,1,,

s2gj8,21,,,,,,Gauss C.F.,,,Résolution numérique des équations trinomes,Nouv. Ann. Math.,10,,,1851,165,174,,1,,

s2gj9,21,,,,,,Gautschi W.,Zhang M.,,Computing orthogonal polynomials in Sobolev spaces,Num. Math.,71,,,1995,159,183,,1,,

s2gj10,11,,,,,,Gemignani L.,,,A fast iterative method for determining the stability of a polynomial,J. Comput. Appl. Math.,76,,,1996,1,12,,1,,

s2gj12,30,,,,,,Gemignani L.,,,Polynomial root computation by means of the LR Algorithm,BIT,37,,,1997,333,345,,1,,

s2gj13,30,,,,,,Gemignani L.,,,Computing a Factor of a Polynomial by Means of Multishift LR Algorithms,SIAM J. Matrix Anal. Appl.,19,,,1998,161,181,,1,,

s2gj14,10,11,,,,,Genin Y.V.,,,Euclid Algorithm; Orthogonal Polynomials; and Generalized Routh-Hurwitz Algorithm,Lin. Algebra Appl.,246,,,1996,131,158,,1,,

s2gj15,19,,,,,,Gerhardt C.I.,,,Geschichte der Mathematik in Deutschland,Monat. Kgl. Preuss. Akad. Wiss. Berlin,,,,1870,141,153,,1,,

s2gj16,25,,,,,,Gersten S.M.,Stallings J.R.,,On Gauss' first proof of the fundamental theorem of algebra,Proc. Amer. Math. Soc.,103,,,1988,331,332,,1,,

s2gj17,26,,,,,,Geurts A.J.,,,A Contribution to the Theory of Condition,Num. Math.,39,,,1982,85,96,,1,,

s2gj18,1,13,,,,,Giesen A.,,,Ueber zwei einfache methoden zur Auflösung numerischer Gleichungen,Z. Math. Phys.,23,,,1878,35,46,,1,,

s2gj19,18,,,,,,Gisclard,,,Sur la limite supérieure des racines positives d'une équation,Nouv. Ann. Math.,11,,,1952,107,108,,1,,

s2gj20,19,,,,,,Glage F.,,,Anwendungen der Gruppentheorie auf die irreducibeln Gleichungen von sechsten Grade,Mon. Math. Phys.,11,,,1900,155,169,,1,,

s2gj21,18,,,,,,Glesser P.,,,Majoration de la norme des facteurs d'un polynôme,Annales Fac. Sci. Toulouse Ser. 5,11,,,1990,67,74,,1,,

s2gj22,23,,,,,,Glubrecht H.,,,An electrical Computer for Higher-order Equations,Z. Angew. Phys.,2 No. 1,,,1950,1,12,,1,,

s2gj23,20,,,,,,Goh W.M.Y.,Wimp J.,,The Zero Distribution of the Tricomi-Carlitz Polynomial,Comput. Math. Appl.,33 No. 1/2,,,1997,119,127,,1,,

s2gj24,21,,,,,,Gonchar A.A.,Rakhmanov E.A.,,Equilibrium measure and the distribution of the zeros of extremal polynomials,Math. USSR. Sb.,53,,,1986,119,130,,1,,

s2gj25,10,,,,,,Gonzalez-Vega L. et al,,,Spécialisation de la suite de Sturm et sous-résultants I/II,R.A.I.R.O. Informatique Théor. et Appl.,24,,,1990,561,588,,1,,

s2gj26,10,,,,,,Gonzalez-Vega L. et al,,,Spécialisation de la suite de Sturm et sous-résultants I/II,R.A.I.R.O. Informatique Théor. et Appl.,28,,,1994,1,24,,1,,

s2gj27,28,,,,,,Goodman A.W.,,,On the derivative with respect to a point,Proc. Amer. Math. Soc.,101,,,1987,327,330,,1,,

s2gb1,25,,,,,,Gaal L.,,,"Classical Galois Theory with Examples 4/E",,,Chelsea,New York,1988,,,,1,,

s2gb2,25,,,,,,Galois E.,,,"Abhandlung über die Auflösbarkeit der Gleichungen durch Wurzelgrössen",,,,,1831,,,,1,,

s2aj27,29,,,,,,Antelo E.,Lang T.,Bruguero J.D.,Computation of $\sqrt{x/d}$ in a Very High Radix Combined Division/Square Root Unit with Scaling and Selection by Rounding,IEEE Trans. Computers,47,,,1998,152,161,,1,,

s2aj28,13,,,,,,Arnold V.I.,,,On some topological invariants of algebraic functions,Trans. Moscow Math. Soc,21,,,1970,30,52,,1,,

s2aj29,13,,,,,,Arnold V.I.,,,Topological invariants of algebraic functions. II,Funct. Anal. Appl.,4 No 2,,,1970,1,9,,1,,

s2aj30,19,,,,,,Aronhold S.,,,Remarque sur la résolution des equations biquadratiques,Nouv. Ann. Math.,17,,,1858,391,391,,1,,

s2aj31,19,,,,,,Aronhold S.,,,Bemerkung über die Auflösung der biquadratischen Gleichungen,J. Reine Angew. Math.,52,,,1856,95,96,,1,,

s2aj32,19,,,,,,Arvesú J. et al,,,Jacobi Sobolev type orthogonal polynomials: Second order differential equations and zeros,J. Comput. Appl. Math.,90,,,1998,135,156,,1,,

s2aj33,20,,,,,,Arwin A.,,,über die Kongruenzen von dem fünften und höheren Graden nach einem Prinzahlmodulus,Ark. Mat. Astr. Fys.,14,,,1918,1,46,,1,,

s2aj34,18,,,,,,Ascher M.,,,in Problems and Solutions,Amer. Math. Monthly,77,,,1970,380,380,,1,,

s2aj35,21,,,,,,Astrand J.J.,,,On en ny methode for losning af trinomiske ligninger af n^te grad,Archiv for Mathematik og Naturvidenskab (Oslo),6,,,1881,448,459,,1,,

s2aj36,3,,,,,,Atanassova L.,,,On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane,J. Comput. Appl. Math.,50,,,1994,99,107,,1,,

s2aj37,3,,,,,,Atanassova L.,,,On the R-Order of a Generalization of Single Step Weierstrass Type Methods,Z. Angew. Math. Mech.,76,,,1996,422,424,,1,,

s2aj38,3,,,,,,Atanassova L.Y.,Herzberger J.P.,,Lower bounds for the R-order of convergence of simultaneous inclusion method for polynomial roots and related iteration methods,J. Comput. Appl. Math.,60,,,1995,3,12,,1,,

s2aj39,25,,,,,,Ayoub R.,,,Ruffini's contribution to the Quintic,Arch. Hist. Exact Science,23,,,1980,253,277,,1,,

s2aj40,18,,,,,,Aziz A.,Ahmad N.,,A compact generalization of Walsh's two-circle theorems for polynomials and rational functions,Indian J. Pure Appl. Math.,27,,,1996,785,790,,1,, s2ab1,20,,,,,,Abbot J.A.,Davenport J.H.,,Polynomial factorization: an exploration of Lenstra's algorithm in "EUROCAL '87 LNCS 378" J.H. Davenport ed.,,,Springer-Verlag,New York,1987,391,402,,1,,

s2ab2,1,2,3,,,,Aberth O.,,,"Precision Numerical Analysis",,,Wm. C. Brown,Dubuque Iowa,1988,,,,1,,

s2ab3,7,14,18,,,,Aberth O.,,,"Precision Numerical Analysis",,,Wm. C. Brown,Dubuque Iowa,1988,,,,1,,

s2ab4,2,14,18,,,,Aberth O.,,,"Precise Numerical Methods using C++",,,Academic Press,,1998,,,,1,,

s2bj21,2,7,,,,,Benada Y.,Crouzeix J.P.,Ferland J.A.,Rate of convergence of a generalization of Newton's method,J. Optim. Theory Appl.,78,,,1993,599,604,,1,,

s2bj22,11,,,,,,Benidir M.,Picinbono B.,,Extended table for eliminating the singularities in Routh's array,IEEE Trans. Automat. Control,35,,,1990,218,222,,1,,

s2bj23,19,,,,,,Berwick W.E.H.,,,The Condition that a Quintic Equation Should be Soluble by Radicals,Proc. London Math. Soc. Ser. 2,14,,,1915,301,307,,1,,

s2bj24,19,,,,,,Berwick W.E.H.,,,On Soluble Sextic Equations,Proc. London Math. Soc.,29,,,1927,1,28,,1,,

s2bj26,13,,,,,,Biermann O.,,,über die Bedingungen unter denen eine ganze rationale Function mehrfache Nullstellen besitzt,Mon. Math. Phys.,13,,,1902,351,360,,1,,

s2bj27,19,,,,,,Biernatzki K.L.,,,Die Arithmetik der Chinesen,J. Reine Angew. Math.,52,,,1856,59,94,,1,,

s2bj29,10,,,,,,Bini D.,Gemignani L.,,Fast parallel computation of the polynomial remainder sequence via Bezout and Hankel matrices,SIAM J. Comput.,24,,,1995,63,77,,1,,

s2bj30,10,,,,,,Bini D.,Gemignani L.,,Erratum,SIAM J. Comput.,25,,,1996,1358,1358,,1,,

s2bj31,10,20,,,,,Bini D.,Pan V.Y.,,Polynomial Division and its Computational Complexity,J. Complexity,2,,,1986,179,203,,1,,

s2bj32,4,,,,,,Bini D.,Pan V.Y.,,Graeffe's; Chebyshev-like; and Cardinal's Processes for Splitting a Polynomial into Factors,J. Complexity,12,,,1996,492,511,,1,,

s2bj33,1,2,30,,,,Bini D.,Pan V.Y.,,Computing matrix eigenvalues and polynomial zeros where the output is real,SIAM J. Comput.,27,,,1998,1099,1115,,1,,

s2bj34,31,,,,,,Birkeland R.,,,Résolution de l'équation algébrique trinome par des fonctions hypergéométriques supérieurs,C.R. Acad. Sci. Paris,171,,,1920,778,781,,1,,

s2bj35,19,,,,,,Birkeland R.,,,Résolution de l'équation générale du cinquième degré,C.R. Acad. Sci. Paris,171,,,1920,1047,1049,,1,,

s2bj36,31,,,,,,Birkeland R.,,,Résolution de l'équation algébrique générale par des fonctions hypergéométriques de plusieurs variables,C.R. Acad. Sci. Paris,171,,,1920,1370,1372,,1,,

s2bj37,31,,,,,,Birkeland R.,,,Résolution de l'équation algébrique générale par des fonctions hypergéométriques de plusieurs variables,C.R. Acad. Sci. Paris,172,,,1921,309,311,,1,,

s2bj38,31,,,,,,Birkeland R.,,,Sur la convergence des développements qui expriment les racines de l'équation algébrique générale par une somme de fonctions hypergéométriques de plusieurs variables,C.R. Acad. Sci. Paris,172,,,1921,1155,1158,,1,,

s2bj39,31,,,,,,Birkeland R.,,,Sur la résolution des équations algébriques générales par une somme de fonctions hypergéométriques,C.R. Acad. Sci. Paris,177,,,1923,23,436,,1,,

s2cj17,25,,,,,,Carvallo E.,,,Démonstration du théorème fondamental de la théorie des équations,Nouv. Ann. Math. Ser. 3,10,,,1891,109,110,,1,,

,20,0,0,0,0,0,Schwarz S.,,,On the number of irreducible factors of a polynomial over a finite field.,Czech. Math. J.,11,,,1961,213,225,no note.,1,0,

s2bj40,31,,,,,,Birkeland R.,,,Les équations algébriques et les fonctions hypergéométriques,Avhandlinger Utgitt Av Det Norske Videnskaps Akade,No. 8,,,1927,1,23,,1,,

s2bj41,19,,,,,,Birkeland R.,,,Ueber die Auflösung algebraischer Gleichungen durch hypergeometrisches Funktionen,Math. Z.,26,,,1927,566,578,,1,,

s2bj42,25,,,,,,Birkhoff G.,,,Galois and Group Theory,Osiris,3 pt 1,,,1937,260,268,,1,,

s2bj43,20,,,,,,Blokh E.L.,,,Method of Decoding Bose-Chauduri Triple Error Correcting Codes,Engineering Cybernetics,3,,,1964,23,32,,1,,

s2bj44,27,,,,,,Bogomolny E.,Bohias O.,Leboeuf P.,Distribution of roots of random polynomials,Phys. Rev. Lett.,68,,,1992,2726,2729,,1,,

s2bj45,18,,,,,,Bojanov B.,,,On an estimation of the roots of algebraic equations,Zastos. Mat.,11,,,1970,195,205,,1,,

s2bj46,25,,,,,,Bolza O.,,,On the Theory of Substitution-Groups and its Application to Algebraic Equations,Amer. J. Math.,13,,,1891,59,142,,1,,

s2bj47,10,,,,,,Bonnet,,,Démonstration Simple du Théorème de Fourier,Nouv. Ann. Math. Ser.1,3,,,,119,121,,1,,

s2bj48,19,,,,,,Bonnet Q.,,,Note sur la détermination approximative des racines imaginaires d'une équation algébrique ou transcendante,Nouv. Ann. Math.,12,,,1853,243,256,,1,,

s2bj49,28,,,,,,Borcea I.,,,On the Sendov Conjecture for Polynomials with at Most Six Distinct Roots,J. Math. Anal. Appl.,200,,,1996,182,206,,1,,

s2bj50,19,,,,,,Bortolotti E.,,,Origine e primo inizio del calcolo degli imaginari,Scientia,33 Supp.,,,1923,71,80,,1,,

s2bj51,19,,,,,,Bortolotti E.,,,L'Algebre nella Scuola matematica bolognese del secolo XVI,Period. Mat. Ser. 4,5,,,1925,147,184,,1,,

s2bj52,19,,,,,,Bortolotti E.,,,Sulla scoperta della risoluzione algebrica delle equazioni del quarto grado,Period. Mat. Ser. 4,6,,,1926,13,16,,1,,

s2bj53,21,,,,,,Borwein P.B.,,,Zeros of Chebyshev polynomials in Markov systems,J. Approx. Theory,63,,,1990,56,64,,1,,

s2bj54,19,,,,,,Bosmans M.H.,,,La résolution de l'équation du 4^e degré chez Simon Stevin,Mathesis,39,,,1925,49,55,,1,,

s2bj55,19,,,,,,Bosmans M.H.,,,La résolution de l'équation du 4^e degré chez Simon Stevin,Mathesis,39,,,1925,99,104,,1,,

s2bj56,19,,,,,,Bosmans M.H.,,,La résolution de l'équation du 4^e degré chez Simon Stevin,Mathesis,39,,,1925,146,153,,1,,

s2bj57,19,25,,,,,Bosmans R.P.H.,,,Albert Girard et Viète a propos de la théorie de la "Syncrèse" de ce dernier,Annales de la Societe Scientifique de Bruxelles,45,,,1926,35,42,,1,,

s2bj58,29,,,,,,Bouton C.L.,,,Discussion of a method for finding numerical square roots,Ann. Math. Ser. 2,10,,,1909,167,172,,1,,

s2bj59,18,,,,,,Bret M.,,,Théorèmes nouveaux sur les limites extrêmes des racines des équations numériques,Ann. Math. Pures Appl.,6,,,1815,112,122,,1,,

s2bj60,21,,,,,,Brezinski C.,Redivo,Zaglia M.,On the zeros of various kinds of orthogonal polynomials,Ann. Numer. Math.,4,,,1997,67,68,,1,,

s2bj61,20,21,,,,,Brillhart J.,,,Some Modular Results on the Euler and Bernouilli polynomials,Acta Arith.,21,,,1972,173,181,,1,,

s2bj62,20,,,,,,Brillhart J.,,,Note on irreducibility testing,Math. Comp.,35,,,1980,1379,1381,,1,,

s2bj63,20,,,,,,Brillhart J.,Filaseta M.,Odlyzko A.,On an irreducibility theorem of A. Cohn,Canad. J. Math.,33,,,1981,1055,1059,,1,,

s2bj64,19,,,,,,Brioschi F.,,,Sur une classe de résolventes de l'équation du cinquième dégré,C.R. Acad. Sci. Paris,63,,,1866,685,688,,1,,

s2bj65,19,,,,,,Brioschi F.,,,Sur une classe de résolventes de l'équation du cinquième dégré,C.R. Acad. Sci. Paris,63,,,1866,785,788,,1,,

s2bj66,19,,,,,,Brioschi F.,,,Sur la résolution de l'équation du cinquième degré,C.R. Acad. Sci. Paris,85,,,1877,1000,1002,,1,,

s2bj67,19,,,,,,Brioschi F.,,,Ueber die Auflösung der Gleichungen von fünften Graden,Math. Ann.,13,,,1879,109,160,,1,,

s2bj68,19,,,,,,Brioschi F.,,,Sur l'équation du Sixième Degré,Acta Math.,12,,,1888,83,101,,1,,

s2bj69,19,,,,,,Brioschi F.,,,Sur l'équation du sixième degré,Ann. Sci. Ecole Norm. Sup. Ser. 3,12,,,1895,343,343,,1,,

s2bj70,29,,,,,,Bromwich T.J.,,,The methods used by Archimedes for approximating to square roots,Math. Gaz.,14,,,1928,253,257,,1,,

s2bj71,20,29,,,,,Brown E.,,,The first proof of the quadratic reciprocity law revisited,Amer. Math. Monthly,88,,,1981,257,264,,1,,

s2bj72,28,,,,,,Brown J.E.,,,On the Sendov conjecture for sixth degree polynomials,Proc. Amer. Math. Soc.,113,,,1991,939,946,Relationship with zeros of derivative,1,,

s2bj73,10,20,,,,,Brown W.S.,Traub J.F.,,Applications of symbolic algebraic computation,Comput. Phys. Comm.,17,,,1979,207,215,,1,,

s2bj74,30,,,,,,Brugnano L.,,,An Algorithm for Polynomials with Multiple Roots,J. Difference Equations and Appl.,1,,,1995,187,207,,1,,

s2bj75,30,,,,,,Brugnano L.,Trigante D.,,Polynomial Roots: The Ultimate Answer,Lin. Algebra Appl.,225,,,1995,207,219,,1,,

s2bj76,29,,,,,,Bshouty N.H. et al,,,A tight bound for approximating the square root,Inform. Process. Lett.,63,,,1997,211,213,,1,,

s2bj77,28,,,,,,Buhmann M.D.,Rivlin T.J.,,A Gauss-Lucas type theorem on the location of the roots of a polynomial,J. Approx. Theory,67,,,1991,235,238,,1,,

s2bj78,13,,,,,,Burkhardt H.,,,Die Anfänge der Gruppentheorie und Paolo Ruffini,Abhandlungen zur Geschichte der Math. (Leipzig),8,,,1892,121,159,,1,,

s2cj37,19,,,,,,Cayley A.,,,Note on the Jacobian sextic equation,Math. Ann.,30,,,1887,78,84,,1,,

s2cj38,11,,,,,,Cendra H.,Salthu R.,Torresi A.,Finding Nondegenerate Hopf Bifurcation Points for Four-Dimensional Two-parametric Systems,Comput. Math. Appl.,33 No. 12,,,1997,115,124,,1,,

s2cj39,20,,,,,,Chabanne H.,,,Factoring of xⁿ-1and Orthogonalization over Finite Fields of Characteristic 2,Applicable Algebra in Eng. Comm. And Computing,6,,,1995,57,63,,1,,

s2cj40,20,29,,,,,Chang T.H.,,,Lösung der Kongruenz x² ≡ a(mod p) nach einem Primzahlmodul p = 4n+1,Math. Nachr.,22,,,1960,136,142,,1,,

s2cj41,10,20,,,,,Char B.W.,Geddes K.O.,Gonnet G.H.,GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation,J. Symb. Comput.,7,,,1989,31,48,,1,,

s2cj42,29,,,,,,Chen C.R.,,,Automatic computation of exponentials; logarithm; ratios and square roots,IBM J. Res. Develop.,16,,,1972,380,388,,1,,

s2cj43,2,,,,,,Chen T.C.,,,Globally convergent polynomial iterative zero finding using APL in "APL 92 Conference Proc.",APL Quote Quod,23 No. 1,,,1992,52,59,,1,,

s2cj44,2,7,15,,,,Chen T.C.,,,Symmetry and Non-convergence in Iterative Polynomial Zero-Finding,SIGNUM,32 Nos. 1/2,,,1997,40,43,,1,,

s2cj45,18,28,,,,,Chen W.,,,On the Polynomials with All Their Zeros on the Unit Circle,J. Math. Anal. Appl.,190,,,1995,714,724,,1,,

s2cj46,21,,,,,,Chen Y.,Ismail M.E.H.,,Asymptotics of extreme zeros of the Meixner Pollaczek polynomials,J. Comput. Appl. Math.,82,,,1997,59,78,,1,,

s2cj47,2,31,,,,,Chio F.,,,Recherches sur la série de Lagrange,Mem.Acad. Sci. Inst. Imp. France,12,,,1854,340,468,,1,,

s2cj48,25,,,,,,Chisini O.,,,Una rapida visione geometrica del teorema fondamentale dell'Algebra,Period. Mat. Ser. 4,2,,,1922,55,59,,1,,

s2cj49,20,,,,,,Chor B.,Rivest R.L.,,A knapsack type public key cryptosystem based on arithmetic on finite fields,IEEE Trans. Inform. Theory,34,,,1988,901,909,,1,,

s2cj50,23,,,,,,Choudhury A.K.,,,The Isograph; an electronic root-finder,Indian J. Phys.,29,,,1955,468,473,,1,,

s2cj51,13,18,,,,,Christie J.R.,,,On the Extension of Budan's Criterion for the Imaginary Roots...,Phil. Mag.,21,,,1842,96,101,,1,,

s2cj52,20,,,,,,Church R.,,,Tables of irreducible polynomials for the first four prime moluli,Ann. of Math.,36,,,1935,198,209,,1,,

s2cj53,29,,,,,,Ciminiera L.,Montuschi P.,,Higher radix square rooting,IEEE Trans. Comput.,39,,,1990,1220,1231,,1,,

s2cj54,20,,,,,,Cipolla M.,,,Sulla risoluzione apiristica delle congruenze binomic secondo un modulo primo,Math. Ann.,63,,,1907,54,61,,1,,

s2cj55,20,,,,,,Cipolla M.,,,Sulle funzioni simmetriche delle soluzioni comuni a piu congruenze secondo un modulo primo,Period. Mat.,22,,,1907,36,41,,1,,

s2cj56,20,,,,,,Cipolla M.,,,Formule di risoluzione aprisitica delle equazioni di grado qualunque in un corpo finito,Rend. Circ. Mat. Palermo,54,,,1930,199,206,,1,,

s2cj77,19,,,,,,Cockle J.,,,Sketch of a Theory of Transcendental Roots,Phil. Mag. Ser. 4,20,,,1860,145,148,,1,,

s2cj78,19,,,,,,Cockle J.,,,Note on Transcendental Roots,Phil. Mag. Ser. 4,20,,,1860,369,373,,1,,

s2cj79,25,,,,,,Cockle J.,,,Note on the Remarks of Mr. Jerrard,Phil. Mag. Ser. 4,21,,,1861,90,92,,1,,

s2cj80,13,,,,,,Cockle J.,,,On Transcendental and Algebraic Solution,Phil. Mag. Ser. 4,21,,,1861,379,383,,1,,

s2cj81,19,,,,,,Cockle J.,,,On Transcendental and Algebraic Solution. Supplementary Paper,Phil. Mag. Ser. 4,23,,,1862,135,139,,1,,

s2cj82,19,25,,,,,Cockle J.,,,Concluding Remarks,Phil. Mag. Ser. 4,26,,,,223,224,,1,,

s2cj83,29,,,,,,Cogwill D.,,,Logic equations for a built-in square root method,IEEE Trans. Computers,13,,,1964,156,157,,1,,

s2cj84,28,,,,,,Cohen G.L.,Smith G.H.,,A proof of Ilieff's conjecture for polynomials with four zeros,Elem. Math,43,,,1988,18,21,,1,,

s2cj85,20,,,,,,Cohen P.J.,,,Decision Procedures for Real and p-adic Fields,Comm. Pure Appl. Math.,22,,,1969,131,151,,1,,

s2cj86,20,,,,,,Cohen S.D.,,,Primitive roots in the quadratic extension of a finite field,J. London Math. Soc.,27,,,1983,221,228,,1,,

s2cj87,20,,,,,,Cohen S.D.,,,Primitve elements and polynomials with arbitrary trace,Discrete Math.,83,,,1990,1,7,,1,,

s2cj88,19,,,,,,Cole F.N.,,,Note on the substitution groups of six; seven; and eight letters,Bull. New York Math. Soc.,2,,,1893,184,190,,1,,

s2cj89,7,,,,,,Collins I.,,,Concerning the Resolution of Equations in Numbers,Philos. Trans. Roy. Soc. London,4,,,1669,929,934,,1,,

s2cj90,18,,,,,,Constantinescu F.,,,Relations entre les coefficients de deux polynômes dont les racines se séparent,Casopis Pest. Mat.,89,,,1964,1,4,,1,,

s2cj91,20,,,,,,Cordone G.,,,Sulla congruenza generale di 4⁰ grado secondo un modulo primo,Rend. Circ. Math. Palermo,9,,,1895,209,243,,1,,

s2cj92,3,,,,,,Cosnard M.,Fraigniaud P.,,Analysis of asynchronous polynomial root-finding methods on a distributed memory multicomputer,IEEE Trans. Parallel Distrib. Syst.,5,,,1994,639,648,,1,,

s2cj93,10,,,,,,Crelle A.L.,,,Die Sätze von Fourier und Sturm zur Theorie der algebraischen Gleichungen,J. Reine Angew. Math.,13,,,1835,119,144,,1,,

s2dj10,10,,,,,,Decker T.,Krandick W.,,Parallel Real Root Isolation,SIGSAM Bull.,32 No. 2,,,1998,53,54,,1,,

s2dj11,20,,,,,,Demeczky M.,,,Ein Beitrag zur Theorie der Congruenzen Höheren Grades,Mathematische und Naturwissenschaftliche Berichte ,8,,,1891,51,59,,1,,

s2eb22,13,,,,,,Eytelwein J.A.,,,"Anweisung zur Auflösung der höhern numerischen Gleichungen",,,,Berlin,1837,,,,1,,

s2fj1,13,,,,,,Faà de Bruno F.,,,Sur une nouveau procédé pour reconnaître immédiatement dans certains cas l'existence de racines imaginaires dans une équation numérique,J. Math. Pures Appl.,15,,,1850,363,364,,1,,

s2fj2,7,,,,,,Falk S.,,,Eine Verallegemainerung der Regula falsi,Z. Angew. Math. Mech.,75 Supp.,,,1995,629,630,,1,,

s2fj3,27,,,,,,Farahmand K.,,,On the average number of real roots of a random algebraic equation,Ann. Probab.,14,,,1986,702,709,,1,,

s2fj4,27,,,,,,Farahmand K.,,,Correction,Ann. Probab.,15,,,1987,1230,1230,,1,,

s2fj5,27,,,,,,Farahmand K.,,,The average number of level crossings of a random algebraic polynomial,Stochastic Anal. Appl.,6,,,1988,247,272,,1,,

s2fj6,27,,,,,,Farahmand K.,,,Real zeros of random algebraic polynomials,Proc. Amer. Math. Soc.,113,,,1991,1077,1084,,1,,

s2fj7,27,,,,,,Farahmand K.,,,Complex Roots of a Random Algebraic Polynomial,J. Math. Anal. Appl.,210,,,1997,724,730,,1,,

s2fj8,27,,,,,,Farahmand K.,,,On the Number of Real Solutions of a Random Polynomial,J. Math. Anal. Appl.,213,,,1997,229,249,,1,,

s2fj9,27,,,,,,Farahmand K.,Jahangiri J.M.,,Complex Roots of a Class of Random Algebraic Polynomials,J. Math. Anal. Appl.,226,,,1998,220,228,,1,,

s2fj10,27,,,,,,Farahmand K.,Smith N.H.,,An Approximate Formula for the Expected Number of Real Zeros of a Random Polynomial,J. Math. Anal. Appl.,188,,,1994,151,157,,1,,

s2fj11,27,,,,,,Farahmand K.,Smith N.H.,,On the Expected Number of Level Crossings of a Random Polynomial,J. Math. Anal. Appl.,208,,,1997,205,217,,1,,

s2fj12,21,,,,,,Farkas J.,,,Auflösung der dreigliedrigen algebraischen Gleichungen,Arch. Math. Phys.,64,,,1879,24,29,,1,,

s2fj13,17,,,,,,Farouki R.T.,Goodman T.N.T.,,On the optimal stability of the Bernstein Basis,Math. Comp.,65,,,1996,1553,1566,,1,,

s2fj14,19,,,,,,Faucette W.M.,,,A Geometric Interpretation of the Solution of the General Quartic Polynomial,Amer. Math. Monthly,103,,,1996,51,57,,1,,

s2fj15,19,,,,,,Faure,,,Sur l'équation du troisième degré et sur une équation du dixième degré de Jacobi,Nouv. Ann. Math. Ser. 2,3,,,1864,116,121,,1,,

s2fj16,19,,,,,,Fayolle,,,On Varignon's method of solving equations of the second degree,Phil. Mag. Ser. 2,4,,,1828,314,314,,1,,

s2fj17,19,,,,,,Fayolle,,,On a method of Laplace of solving equations of the third degree,Phil. Mag. Ser. 2,4,,,1828,462,463,,1,,

s2fj18,13,,,,,,Fdil A.,,,A new method for solving a nonlinear equation with error estimations,Appl. Numer. Math.,21,,,1996,417,429,,1,,

s2fj19,21,,,,,,Fejér L.,,,Mechanische Quadraturen mit positiven Coteschen Zahlen,Math. Z.,37,,,1933,287,310,,1,,

s2fj20,30,,,,,,Fiedler M.,,,Expressing a polynomial as the characteristic polynomial of a symmetric matrix,Lin. Algebra Appl.,141,,,1990,265,270,,1,,

s2fj21,20,,,,,,Filaseta M.,,,A further generalization of an irreducibility theorem of A. Cohn,Canad. J. Math.,34,,,1982,1390,1395,,1,,

s2fj22,20,,,,,,Filaseta M.,,,Irreducibility criteria for polynomials with non-negative coefficients,Canad. J. Math.,40,,,1988,339,351,,1,,

s2fj24,20,,,,,,Fleischmann P.,,,Connections bewteen the algorithms of Berlekamp and Niederreiter for factoring polynomials over F_q,Lin. Algebra Appl.,192,,,1993,101,108,,1,,

s2fj25,9,,,,,,Ford J.,,,A generalization of the Jenkins-Traub method,Math. Comp.,31,,,1977,193,203,,1,,

s2fj26,2,24,,,,,Ford W.F.,Pennline J.A.,,Accelerated convergence in Newton's method,SIAM Rev.,38,,,1996,658,659,,1,,

s2fj27,2,10,,,,,Fouret G.,,,Sur la méthode d'approximation de Newton,Nouv. Ann. Math. Ser. 3,9,,,1890,567,585,,1,,

s2fj28,18,,,,,,Fouret G.,,,Sur la détermination d'une limite inférieure des racines d'une équation algébrique,Bull. Soc. Math. France,20,,,1892,4,6,,1,,

s2fj29,10,18,,,,,Fouret G.,,,Sur le théorème de Budan et Fourier,Nouv. Ann. Math. Ser. 3,7,,,1892,82,88,,1,,

s2fj30,2,,,,,,Franklin F.,,,On Newton's Method of Approximation,Amer. J. Math.,4,,,1881,275,276,,1,,

s2fj31,13,,,,,,Froda A.,,,Résolution générale des équations algébriques,C.R. Acad. Sci. Paris,189,,,1929,523,525,,1,,

s2fj32,18,,,,,,Fujii M.,Kubo F.,,Operator Norms as Bounds for Roots of Algebraic Equations,Proc. Japan Acad.,49,,,1973,805,808,,1,,

s2fj33,18,,,,,,Fujii M.,Kubo F.,,Buzano's inequality and bounds for roots of algebraic equations,Proc. Amer. Math. Soc.,117,,,1993,359,361,,1,,

s2fj34,20,29,,,,,Furquim de Almeida F.,,,Sôbre uma formula de Cipolla,Summa Brasil. Math.,1,,,1946,207,219,,1,,

s2fb1,10,25,,,,,Faà de Bruno F.,,,"Théorie Générale de l'élimination",,,,Paris,1859,,,,1,,

s2fb2,10,19,20,25,,,Faddeev D.K.,Sominskii I.S.,,"Problems in Higher Algebra",,,Freeman,San Francisco,1965,,,,1,,

s2fb3,29,,,,,,Fandrianto J.,,,Algorithm for high-speed shared radix-4 division and radix-4 square-root in "Proc. 8th IEEE Symposium on Computer Arithmetic",,,,,1987,73,79,,1,,

s2fb4,29,,,,,,Fandrianto J.,,,Algorithm for High-Speed Shared Radix 8 Division and Radix 8 Square-Root in "Proc. 9th IEEE Symposium on Computer Arithmetic",,,,Santa Monica CA,1989,68,75,,1,,

s2fb5,25,,,,,,Fine B.,Rosenberger G.,,"The Fundamental Theorem of Algebra",,,Springer-Verlag,,1997,,,,1,,

s2gj28,17,,,,,,Goodman T.N.T.,Said H.B.,,Shape preserving properties of the generalized Ball basis,Computer Aided Geometric Design,8,,,1991,115,121,,1,,

s2gj29,15,,,,,,Gordon S.P.,von Eschen E.R.,,A parabolic extension of Newton's method,Inter. J. Math. Ed. Sci. Tech,21,,,1990,519,525,,1,,

s2gj30,29,,,,,,Gosling J.B.,Blakeley C.M.S.,,Arithmetic unit with integral division and square-root,Proc. IEE Part E,134,,,1987,17,23,,1,,

s2gj31,29,,,,,,Gould H.H.,,,Cellular logical array for non-restoring square-root extraction,Electronics Letters,6 No. 3,,,1970,66,67,,1,,

s2gj32,13,,,,,,Gräffe,,,Beweis eines Satzes aus der Theorie der numerischen Gleichungen,J. Reine Angew. Math.,10,,,1832,288,291,,1,,

s2gj33,19,,,,,,Green M.,,,On the analytic solution of the equation of the fifth degree,Compositio Math.,37,,,1978,233,241,,1,,

s2gj34,13,,,,,,Greene D.,,,Method of Solving Numerical Equations,Amer. Math. Monthly,1,,,1859,406,408,,1,,

,21,0,0,0,0,0,Gol'berg E.M.,Malozemov V.N.,,Estimates for the zeros of certain polynomials.,Ves. Lenin. Uni. Mat., Mekh., Astr.,6,,,1979,127,135,Zeros of linear combination of a set of orthogonal polynomials.,1,0,

,28,0,0,0,0,0,Grace J.H.,,,The zeros of a polynomial,Proc. Camb. Phil. Soc.,11,,,1902,352,357,Relation between zeros of a polynomial and those of its derivative.,1,0,

,21,0,0,0,0,0,Craven T.,Csordas G.,,Jensen polynomials and the Turan and Laguerre inequalities.,Pac. J. Math.,136,,,1989,241,260,No note.,1,0,

,10,0,0,0,0,0,Conkwright N.B.,,,An elementary proof of the Budan-Fourier theorem.,Amer. Math. Monthly,50,,,1943,603,605,Number of roots related to series of derivatives.,1,0,

,21,0,0,0,0,0,Dvoretzky A.,,,On sections of power series.,Ann. Math. (Ser. 2),51,,,1950,643,696,No note.,1,0,

,28,0,0,0,0,0,Borcea J.,,,Two approaches to Sendov's conjecture.,Arch. Math.,71,,,1998,46,54,Zeros of derivative of a polynomial.,1,0,

,13,0,0,0,0,0,Ancochea G.,,,Zeros of self-inversive polynomials.,Proc. Amer. Math. Soc.,4,,,1953,900,902,No note.,1,0,

,20,0,0,0,0,0,Cohen S.D.,,,The reducibility theorem for linearised polynomials over finite fields.,Bull. Austral. Math. Soc.,40-3,,,1989,407,412,No note.,1,0,

,2,0,0,0,0,0,Frontini, M.,,,Hermite interpolation and a new iterative method for the computation of the roots of non-linear equations,Calcolo,40,,,2003,109,119,Order 1+ $\sqrt{3}$ with two function evaluations. More efficient than secant.,1,0,

,2,19,0,0,0,0,Buckley J.J.,Eslami E.,,Neural net solutions to fuzzy problems. The quadratic equation.,Fuzzy Sets Syst.,86,,,1997,289,298,Title says it.,1,0,

,2,0,0,0,0,0,Noor M.A.,Gupta V.,,Modified Householder iterative method free from second derivatives for nonlinear equations.,Appl. Math. Comput.,190,,,2007,1701,1706,6th order with four evaluations.,1,0,

,2,0,0,0,0,0,Noor M.A.,Noor K.I.,ul-Hassan M.,Third order iterative methods free from second derivatives for nonlinear equations.,Appl. Math. Comput.,190,,,2007,1551,1556,3rd order with 3 evaluations.,1,0,

,2,0,0,0,0,0,Noor K.I.,Noor M.A.,Momani S.,Modified Householder iterative method for nonlinear equations.,Appl. Math. Comput.,190,,,2007,1534,1539,6th order with 5 evaluations.,1,0,

,25,0,0,0,0,0,Santos J.C.,,,The fundamental theorem of algebra deduced from elementary calculus,Math. Gaz.,91,,,2007,302,303,Existence.,1,0,

,19,0,0,0,0,0,Renfro D.,,,The Hindu method for completing the square.,Math. Gaz.,91,,,2007,198,201,History of quadratics.,1,0,

,21,0,0,0,0,0,DeFazio M.V.,Gupta D.P.,Muldoon M.E.,Limit relations for the complex zeros of Laguerre and q-Laguerre polynomials.,J. Math. Anal. Applics,334,,,2007,977,982,No note.,1,0,

,2,0,0,0,0,0,Chun C.,,,Some improvements of Jarratt's method with sixth-order convergence.,Appl. Math. Comput.,190,,,2007,1432,1437,Sixth order with 4 evaluations.,1,0,

,2,15,0,0,0,0,Elgin D.,,,Newton- Raphson revisited.,Math. Gaz.,91,,,2007,307,312,Gives method using 2nd derivative, of 3rd order.,1,0,

,15,0,0,0,0,0,Kou J.,Wang X.,,Sixth-order variants of Chebyshev-Halley methods for solving nonlinear equations.,Appl. Math. Comput.,190,,,2007,1839,1843,6th order with four evaluations.,1,0,

,25,0,0,0,0,0,Smithies F.,,,A forgotten paper on the fundamental theorem of algebra,Notes Rec. Roy. Soc. London,54,,,2000,333,341,Wood gave an incomplete proof of existence in 1798,1,0,

,10,0,0,0,0,0,Norton G.H.,,,Extending the binary GCD algorithm, in "Algebraic Algorithms and Error-Correcting Codes'',Lec. Notes Comp. Sci.,229,Springer,,1986,363,372,Gives some relatively efficient GCD algorithms,1,0,

,19,0,0,0,0,0,Szenassy B.,,,History of Mathematics in Hungary until the 20'th Century,,,Springer-Verlag,Berlin,1992,0,,Solves quadratic by continued fraction,1,0,

,1,31,0,0,0,0,Boyd J.P.,,,Computing the Zeros, Maxima and Inflection points of Chebyshev, Legendre and Fourier Series: Solving Transcendental Equations by Spectral Interpolation and Polynomial Rootfinding,J. Engin. Math.,56(3),,,2006,203,219,Uses matrix and subdivision methods,1,0,

,3,0,0,0,0,0,Proinov P.,,,A new semilocal convergence theorem for the Weierstrass method from data at one point,C.R. Acad. Bulg. Sci.,59,,,2006,131,136,,1,0,

,3,0,0,0,0,0,Proinov P.,,,Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros,C.R. Acad. Bulg. Sci.,,,,2006,705,712,,1,0,

,2,0,0,0,0,0,Ujevic N.,Erceg G.,Lekic I.,A family of methods for solving nonlinear equations,Appl. Math. Comput.,192,,,2007,311,318,Generalized Newton,1,0,

,2,0,0,0,0,0,Chun C.,Ham Y.,,Some sixth-order variants of Ostrowski's root-finding methods,Appl. Math. Comput.,193,,,2007,389,394,Generalized Newton has 6th order with 4 evaluations,1,0,

,15,0,0,0,0,0,Mir N.A.,Zaman T.,,Some quadrature-based three-step methods for non-linear equations,Appl. Math. Comput.,193,,,2007,366,373,6th-order with 5 evaluations, plus 8th order with 6 evaluations,1,0,

,15,0,0,0,0,0,Javidi M,,,Iterative methods to non-linear equations,Appl. Math. Comput.,193,,,2007,360,365,3rd order with 2nd derivative,1,0,

,15,0,0,0,0,0,Rafiq A.,,,A note on ``new classes of iterative methods for nonlinear equations'' and ``Some iterative methods free from second derivatives for nonlinear equations'',Appl. Math. Comput.,193,,,2007,572,576,Some errors in earlier work of Noor (yet to be published),1,0,

,2,0,0,0,0,0,Kanwar V.,Tomar S.K.,,Modified families of multi-point iterative methods for solving nonlinear equations,Numer. Algs.,44,,,2007,381,389,3rd order without second derivatives,1,0,

,2,0,0,0,0,0,Berger A. et al,,,Newton's Method Obeys Benford's Law,Amer. Math. Monthly,114,,,2007,588,601,Treats size of digits in Newton iterations,1,0,

,32,0,0,0,0,0,Golbabai A.,Javidi M.,,A third-order Newton-type method based on modified homotopy perturbation method,Appl. Math. Comput.,191,,,2007,199,205,Title says it,1,0,

,15,0,0,0,0,0,Rafiq A.,,,A note on `` New family of iterative methods for nonlinear equations'',Appl. Math. Comput.,192,,,2007,280,282,Refers to a paper by Noor: it is less efficient than claimed,1,0,

,21,0,0,0,0,0,Moreno-Balcazar J.J.,,,A note on the zeros of Freud-Sobolev orthogonal polynomials,J. Comput. Appl. Math.,207,,,2007,338,344,Special functions,1,0,

,21,0,0,0,0,0,Marcellan F. et al,,,Electrostatic models for zeros of polynomials: old, new, and some open problems,J. Comput. Appl. Math.,207,,,2007,258,272,Treats special functions,1,0,

,2,15,0,0,0,0,Kanwar V.,Tomar S.K.,,Modified families of Newton, Halley and Chebyshev methods,Appl. Math. Comput.,192,,,2007,20,26,Some methods thrid order,1,0,

,2,0,0,0,0,0,Grau-Sanchez M.,Diaz-Barrero J.-L.,,A Hummel and Seebeck family of iterative methods with improved convergence and efficiency,Appl. Math. Comput.,191,,,2007,263,271,Fifth order with 4 evaluations,1,0,

,3,12,0,0,0,0,Petkovic M. S. et al,,,A posteriori error bound method for the inclusion of polynomial zeros,J. Comput. Appl. Math.,208,,,2007,316,330,Simultaneous interval methods,1,0,

,26,0,0,0,0,0,Winkler J.R.,,,High order terms for condition estimation of univariate polynomials,SIAM J. Sci. Computing,28,,,2007,1420,1436,Treats condition of close roots,1,0,

,32,0,0,0,0,0,Golbabai A.,Javidi M.,,New iterative methods for nonlinear equations by modified HPM,Appl. Math. Comput.,191,,,2007,122,127,Uses homotopy method,1,0,

,15,0,0,0,0,0,Noor M.A.,,,New classes of iterative methods for nonlinear equations,Appl. Math. Comput.,191,,,2007,128,131,Uses second derivative,1,0,

,2,0,0,0,0,0,Chun C.,,,Some variants of Chebyshev-Halley methods free from second derivatives,Appl. Math. Comput.,191,,,2007,193,198,3rd order with 3 evaluations,1,0,

,2,0,0,0,0,0,Chun C.,,,Some second-derivative free variants of Chebyshev-Halley methods,Appl. Math. Comput.,191,,,2007,410,414,Third order with 3 evaluations,1,0,

,2,0,0,0,0,0,Noor M.A.,,,Some iterative methods free from second derivatives for nonlinear equations,Appl. Math. Comput.,192,,,2007,101,106,Appears to be 4th order with 3 evaluations,1,0,

,2,0,0,0,0,0,Kou J.,,,Fourth-order variants of Cauchy's method for solving nonlinear equations,Appl. Math. Comput.,192,,,2007,113,119,4th order with 3 evaluations,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,,A family of new Newton-like methods,Appl. Math. Comput.,192,,,2007,162,167,Allows f'(x) to be close to 0 near a root,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,Some variants of Ostrowski's method with seventh-order convergence,J. Comput. Appl. Math.,209,,,2007,153,159,7th order with 4 evaluations,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,Some modifications of Newton's method with fifth-order convergence,J. Comput. Appl. Math.,209,,,2007,146,152,Fifth order with 4 evaluations,1,0,

,1,0,0,0,0,0,Boyd, J.P.,,,Computing the Zeros of a Fourier series or a Chebyshev series or General Orthogonal Polynomial Series with Parity Symmetries,Comput. Math. Appl.,54,,,2007,336,349,Roots of polynomial written in truncated Chebyshev series etc.,1,0,

,13,0,,0,0,0,Schmeisser G.,,,Orthogonal expansion of real polynomials, location of zeros, and an L² inequality,J. Approx. Theory,109,,,2001,126,147,,1,0,

,20,29,0,0,0,0,Lindhurst S.,,,An analysis of Shank's algorithm for computing square roots in finite fields, in "Proc. 5th Conf. Canadian number theory Ass.",,,,,1995,0,0,Tiltle says it,1,0,

,25,0,0,0,0,0,Houzel C.,,,The Work of Niels Henrik Abel, in "The Legacy of Niels Henrik Abel", O.A. Laudal, R. Piene (eds),,,,Berlin,2004,49,65,Impossibility of solution by radicals,1,0,

,25,0,0,0,0,0,Lazard D.,,,Solving quintics in radicals, in "The Legacy of Niels Henrik Abel", O.A. Laudal, R. Piene (eds),,,,Berlin,2004,207,225,Title says it,1,0,

,19,0,0,0,0,0,Spearman, B.K.,Williams, K.S.,,On solvable quintics X ⁵+ aX + b and X⁵ + aX² + b,Rocky Mtn.J, Math.,26,,,1996,753,772,There are an infinite number of the first type, but only five of the second,1,0,

,19,25,0,0,0,0,Alten H.W. et al,,,4000 Jahre Algebra,,,,Berlin,2003,0,0,Treats low-degree polys, existence, solution by radicals,1,0,

,25,0,0,0,0,0,Radloff I.,,,Evariste Galois: Principles and Applications,Hist. Math.,29,,,2002,114,137,Considers which equations are soluble by radicals,1,0,

,1,0,0,0,0,0,Traub J.F.,Woźniakowski H.,,A General Theory of Optimal Algorithms,,,Academic Press,New York,1980,0,0,Treats bisection.,1,0,

,10,0,0,0,0,0,Abdeljaoued J.,Diaz-Toca G.M.,Gonzalez-Vega L.,Minor of Bezout matrices, subresultants, and parameterization of the degree of the polynomial greatest common divisor.,Int. J. Comput. Math.,81-10,,,2004,1223,1238,No note.,1,0,

,21,0,0,0,0,0,Yildirim C.Y.,,,On the zeros of the sections of the exponential function.,Turk. J. Math. Ser. 3,16,,,1992,177,182,No note.,1,0,

,28,0,0,0,0,0,Walsh J.L.,,,The location of critical points,Amer. Math. Soc. Colloq. Publ.,34,,,1950,0,0,Treats relation between zeros of a polynomial and those of its derivative.,1,0,

s2pj45,19,,,,,,Pokorny M.,,,Ueber die biquadratische Gleichungen,Z. Math. Phys.,10,,,1865,320,321,,1,,

s2pj46,13,,,,,,Poletti G.,,,Nuovo metodo per determinare le radici imaginarie..,Mem. Accad. Sci. Torini,30,,,1824,49,80,see also ibid Vol 35 pp 79-94,1,,

s2pj47,19,20,,,,,Polkinghorn F.,Jr.,,Decoding of double and triple error correcting Bose-Chauduri codes,IEEE Trans. Inform. Theory,12,,,1966,480,481,,1,,

s2pj48,18,,,,,,Popoviciu T.,,,Sur les equations algebriques ayant toutes leurs racines reelles,Mathematica (Cluj),9,,,1935,129,145,,1,,

s2pj49,13,,,,,,Popper J.,,,Beiträge zu Weddle's Methode der Auflösung numerischer Gleichungen,Z. Math. Phys.,7,,,1862,384,397,,1,,

s2pj50,7,,,,,,Potra F.,Qi L.,Sun D.,Secant methods for semismooth equations,Numer. Math.,80,,,1998,305,324,,1,,

s2pj51,10,,,,,,Poulain,,,Théorèmes sur les équations algébriques et les fonctions quadratiques de Campbell,C.R. Acad. Sci. Paris,106,,,1888,470,473,,1,,

s2pj52,29,,,,,,Prado J.,Alcantara R.,,A fast square-rooting algorithm using a digital signal processor,Proc. IEEE,75,,,1987,262,264,,1,,

s2pj53,10,,,,,,Pre\v{s}ic M.,,,A Method for solving equations in finite fields,Mat. Vesnik,7,,,1970,507,509,,1,,

s2pj54,3,,,,,,Pre\v{s}ic M.,,,A convergence theorem for a method for simultaneous determination of all zeros of a polynomial,Publ. Inst. Math. (Beograd),28 No. 5,,,1980,159,165,,1,,

s2pj55,19,,,,,,Pritchard E.A.,,,An Algorithm for Solving Cubic Equations,Math. Gaz.,79,,,1995,350,352,,1,,

s2pb1,11,,,,,,Pal D.,Kailath T.,,A Generalization of the Schur-Cohn Test: The Singular Cases in "Proc. 33rd Midwest Symposium on Circuits and Systems",,,,Calgary Alberta,1990,64,67,,1,,

s2pb2,17,,,,,,Pan V.Y.,,,Computational Complexity of Computing Polynomials over the Fields of Real and Complex Numbers in "Proc. 10th Annual ACM Symp. on Theory of Computing",,,ACM Press,New York,1978,162,172,,1,,

s2pb3,2,5,,,,,Pan V.Y.,,,New Techniques for Approximating Polynomial Zeros in "Proc. 5th Annual ACM-SIAM Symp. on Discrete Algorithms",,,ACM Press,New York,1994,260,270,,1,,

s2pb4,13,,,,,,Pan V.Y.,,,Improved algorithms for approximating polynomial zeros in "Proc. of the 27th ACM Symposium on Theory of Computing",,,,Las Vegas NV,1995,,,,1,,

s2pb5,5,13,,,,,Pan V.Y.,,,Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros in "Proc. 27th Annual ACM Symposium on Theory of Computing",,,ACM Press,New York,1995,741,750,,1,,

s2pb6,4,5,16,,,,Pan V.,Reif J.H.,,Some polynomial and Toeplitz matrix computations in "Proc. 28th Annual IEEE Symp. on Foundations of Computer Science",,,,,1987,173,184,,1,,

s2pb7,1,2,6,7,14,24,Patel V.A.,,,"Numerical Analysis",,,Saunders College,,1994,,,,1,,

s2pb8,26,,,,,,Patel V.A.,,,"Numerical Analysis",,,Saunders College,,1994,,,,1,,

s2pb9,24,,,,,,Paterson A.,,,"Differential Equations and Numerical Analysis ",,,Cambridge Univ. Press,,1991,,,,1,,

s2pb10,1,2,4,29,,,Pennington R.H.,,,"Introductory Computer Methods and Numerical Analysis",,,Macmillan,New York,1965,,,,1,,

s2pb11,2,14,15,30,,,Penny J.,Lindfield G.,,"Numerical Methods Using Matlab",,,Ellis Horwood,New York,1995,,,,1,,

s2pb13,2,7,10,19,25,,Petersen J.,,,"Theorie der algebraischen Gleichungen",,,Host and Son,Kopenhagen,1878,,,,1,,

s2pb14,20,,,,,,Peterson W.W.,Weldon E.J.,,"Error Correcting Codes 2nd ed.",,,M.I.T. Press,Cambridge Mass,1972,,,,1,,

s2pb15,10,17,,,,,Petkov N.,,,"Systolic Parallel Processing; Chap. 7",,,North-Holland,,1993,,,,1,,

s2pb16,3,12,15,,,,Petkovi\'{c} L.D.,,,The analysis of the numerical stability of iterative methods using interval arithmetic in: L. Atanassova and J. Herzberger Eds. "Computer Arithmetic and Enclosure Methods; Proc. of Conference SCAN-91; Oldenburg (1991)",,,North-Holland,Amsterdam,1992,309,317,,1,,

s2pb17,7,,,,,,Petkovi\'{c} L.,Tri\v{c}kovi\'{c} S.,\v{Z}ivcovi\'{c} D.,Secant Slope Method for Inclusion of Complex Zeros of Polynomials in "Numerical Methods and Error Bounds" ed G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,172,177,,1,,

s2pb18,3,,,,,,Petkovi\'{c} M.S.,,,Some classes of iterative methods for finding zeros of polynomials and analytic functions in "World Congress of Nonlinear Analysts" ed. V. Lakshmikantham,,,Walter de Gruyter,Berlin,1995,3859,3870,,1,,

s2pb19,3,12,,,,,Petkovi\'{c} M.S.,,,Asynchronous Methods for Simultaneous Inclusion of Polynomial Roots in "Numerical Methods and Error Bounds" ed. G. Alfeld and J. Herzberger,,,Akademie Verlag,,1996,178,187,,1,,

s2pb20,4,,,,,,Piller M.,,,"Die Auflösung der höheren numerischen Gleichungen durch successives Quadriren der Wurzeln",,,,Dillingen,1862,,,,1,,

s2pb21,20,,,,,,Pinch R.G.E.,,,Recognizing elements of finite fields in "Cryptography and Coding II" Ed. C. Mitchell,,,,Oxford,1992,193,197,,1,,

s2pb22,10,12,,,,,Pinkert J.R.,,,interval Arithmetic Applied to Polynomial Remainder Sequences in "ACM Symp. on Symbolic and Algebraic Computation",,,Ass. Comp. Mach.,New York,1976,214,215,,1,,

s2pb24,19,25,,,,,Postnikov M.M.,,,"Foundations of Galois Theory",,,Pergamon Press,,1962,,,,1,,

s2pb25,1,7,,,,,Potra F.A.,Shi Y.,,A Note on Brent's Rootfinding Method in "Numerical Methods and Error Bounds" ed G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,188,197,,1,,

s2pb26,19,,,,,,Prasolov V.,Solovyev Y.,,"Elliptic Functions and Elliptic Integrals",,,Amer. Math. Soc.,,1997,,,,1,,

s2pb27,19,29,,,,,Pratt O.,,,"New and easy method of solution of the cubic and biquadratic equations",,,Longmans,London,1866,,,,1,,

s2rj1,20,,,,,,Rados G.,,,Ein Satz über Konguenzen höheren grades,Acta Scientiarum Math.,1,,,1922,1,5,,1,,

s2rj2,20,,,,,,Rados G.,,,über Kongruenzbedingungen der rationalen Lösbarkeit von algebraischen Gleichungen,Math. Ann.,87,,,1922,78,81,,1,,

s2rj3,19,,,,,,Radford M.,,,On the Solution of Certain Equations of the Seventh Degree,Quart. J. Math.,30,,,1898,263,306,,1,,

s2rj4,18,,,,,,Rahman Q.,,,A bound for the moduli of the zeros of polynomials,Canad. Math. Bull.,13,,,1970,541,542,,1,,

s2rj5,29,,,,,,Ramamoorthy C.V.,Goodman J.B.,Kim K.H.,Some properties of iterative square-rooting methods using high-speed multiplication,IEEE Trans. Comput.,21,,,1972,837,847,,1,,

s2rj6,2,19,,,,,Rashed R.,,,Résolution des équations numériques et algèbre: Sharaf-al-Din al-Tusi; Viète,Arch. Hist. Exact Science,12,,,1974,244,290,,1,,

s2rj7,19,,,,,,Rashed R.,,,Les travaux perdus de Diophante,Revue d'Histoire des Sciences,27,,,1974,97,122,see also ibid Vol. 28 no. 1 pp 3-30,1,,

s2rj8,29,,,,,,Rashed R.,,,L'Extraction de la racine n^ième et l'Invention des Fractions Décimales (XI^e-XII^e Siècles),Arch. Hist. Exact Science,18,,,1978,191,243,,1,,

s2rj9,28,,,,,,Rassias M. Th.,,,Zeros of polynomials and their derivative,Rev. Roumaine Math. Pures Appl.,36,,,1991,441,448,,1,,

s2rj10,18,,,,,,Reich S.,,,in Problems and Solutions,Amer. Math. Monthly,77,,,1970,655,655,,1,,

s2rj11,20,,,,,,Redei L.,,,A short proof of a theorem of St. Schwarz concerning finite fields,Casopis Pest. Mat. Fys.,75,,,1950,211,212,,1,,

s2rj12,20,29,,,,,Reed I.S.,Truong T.K.,Miller R.L.,Fast algorithm for computing a primitive 2^p+1th root of unity in GF[(2^p-1)²],Electron. Lett.,14,,,1978,493,494,,1,,

s2rj13,19,,,,,,Reidt F.,,,Ueber irreducible cubische Gleichungen,Z. Math. Phys.,17,,,1872,430,432,,1,,

s2rj14,16,,,,,,Renegar J.,,,On the Computational Complexity of Approximating Solutions for Real Algebraic Formulas,SIAM J. Comput.,21,,,1992,1008,1025,,1,,

s2rj15,21,,,,,,Ricci P.E.,,,Improving the Asymptotics for the Greatest Zeros of Hermite Polynomials,Comput. Math. Appl.,30 No. 3/6,,,1995,409,416,,1,,

s2rj16,26,,,,,,Rice J.R.,,,A Theory of Condition,SIAM J. Numer. Anal.,3,,,1966,287,310,,1,,

s2rj17,2,,,,,,Richard J.,,,Sur la methode d'approximation de Newton,Rev. Math. Spec.,8,,,1905,137,138,,1,,

s2rj18,17,,,,,,Richman P.L.,,,Automatic Error Analysis for Determining Precision,Comm. ACM,15,,,1972,813,817,,1,,

s2rb6,28,,,,,,Rassias M. Th.,,,On polynomial inequalities and extremal problems in "General Inequalities 6",,,Birkhauser Verlag,Basel,1992,161,174,,1,,

s2rb7,28,,,,,,Rassias M. Th.,Srivastava H.M.,,Some recent advances in the theory of the zeros and critical points of a polynomial in "Topics in Polynomials of One and Several Variables and Their Applications" ed. Th. M. Rassias H. Srivistava and A. Yanushauskas,,,World Scientific,Singapore,1993,463,481,,1,,

s2rb8,13,,,,,,Ratschek H.,Rokne J.,,"Computer Methods for the Range of Functions",,,Ellis Horwood,Chichester,1984,137,141,,1,,

s2rb9,19,20,,,,,Redei L.,,,"Algebra",,,Pergamon Press,London,1967,,,,1,,

s2rb10,2,4,10,,,,Reif J.,,,An O(nlog³n) Algorithm for Real Root Problem in "Proc. 34-th Annual IEEE Symp. on Foundations of Computer Science",,,,,1993,626,635,,1,,

s2rb11,10,,,,,,Reif J.H.,,,Work efficient parallel solution of Toeplitz systems and polynomial GCD in "27th Annual ACM Symposium on Theory of Computing",,,,Las Vegas NV,1995,751,760,,1,,

s2rb12,20,,,,,,Rhee M.Y.,,,"Error-Correcting Codes",,,McGraw-Hill,,1989,,,,1,,

s2rb13,2,29,,,,,Rigaud S.J.,,,"Correspondence of Scientific Men Vols. I and II",,,Georg Olms,Hildesheim,1965,372,372,,1,,

s2rb14,20,,,,,,Roman S.,,,"Coding and information theory; Graduate Texts in Mathematics Vol. 134",,,Springer,New York,1992,,,,1,,

s2rb15,20,,,,,,Rónyai L.,,,Factoring polynomials over finite fields in "Proc. 28th Ann. Symp. Found. Comput. Sci",,,IEEE Press,,1987,132,137,,1,,

s2rb16,19,,,,,,Rosen F.,,,"The Algebra of Mohammed ben Musa",,,,London,1831,,,,1,,

s2rb17,25,,,,,,Rotman J.J.,,,"Galois Theory",,,Springer-Verlag,,1990,,,,1,,

s2rb18,19,,,,,,Rouget J.,,,"Règles practiques pour opérer la séparation immédiate des racines réelles...",,,Gauthier-Villars,Paris,1807,,,,1,,

s2rb19,19,25,,,,,Rouse Ball W.W.,,,"A Short Account of the History of Mathematics 6th Edition",,,,London,1915,,,,1,,

s2rb20,13,29,,,,,Ruchonnet C.,,,"éléments de calcul approximatif",,,Gauthier-Villars,Paris,1887,,,,1,,

s2rb21,21,,,,,,Rutherford W.,,,"The Complete Solution of Numerical Equations in which by one Uniform Process the Imaginary as well as the Real Roots are easily determined",,,G. Bell,London,1848,,,,1,,

s2rb22,2,4,7,,,,Rutishauser H.,,,"Vorlesungen über Numerische Mathematik Vol. 1",,,Birkhauser,Stuttgart,1976,,,,1,,

s2rb23,2,4,7,,,,Rutishauser H.,,,"Lectures on Numerical Mathematics",,,Birkhauser,Boston,1990,,,,1,,

,21,0,0,0,0,0,McKeon D.G.C.,Sherry T.N.,,Exploring cyclotomic polys,Math. Gaz.,85,,,2001,59,65,Considers polys whose roots are cos(qπ/p) (q=1,…,p-1),1,0,

,17,0,0,0,0,0,Aldaz M. et al,,,A new method to obtain lower bounds for polynomial evaluation,Theoret. Comput. Sci.,259,,,2001,577,596,,1,0,

,19,13,29,0,0,0,Al-Kashi,,,Miftah al-Hisab,,,,,0,0,0,Arabic treatment of Horner's method and square roots,1,0,

,2,16,0,0,0,0,Traub J.F.,,,Parallel Algorithms and Parallel Computational Complexity, in "Proc. IFIP Congress '74",North Holland,,,,1974,685,687,,1,0,

,3,0,0,0,0,0,Kanno S.,Kjurkchiev N.V.,Yamamoto T.,On Some Methods for the Simultaneous Determination of Polynomial Zeros,Japan J. Indust. Appl. Math.,13,,,1996,267,288,Shows an SOR-like acceleration of the Durand-Kerner method.,1,0,

,13,10,0,0,0,0,Knebush M.,Schneider C.,,Einfuhrung in die reelle algebre,,,Vieweg,Braunschweig,1989,0,0,,1,0,

,20,0,0,0,0,0,Bonorden O. et al.,,,Factoring a binary polynomial of degree over one million,SIGSAM Bull.,35(1),,,2001,16,18,Uses Bipolar and a parallel version of Cantor's multiplication algorithm.,1,0,

,18,0,0,0,0,0,Jain V.K.,,,On Cauchy's bound for the moduli of zeros of a polynomial,Indian J. Pure Appl. Math.,31,,,2000,957,966,A bound using |a_n-1| and Max_0≤j≤n-2|a_j| gives better results than many known bounds.,1,0,

,19,29,0,0,0,0,Kangshen S.,Crossley J.N.,Lun A.W.C.,The Nine Chapters on the Mathematical Art: Companion and Commentary,,,Oxford University Press,Oxford,1999,0,0,Modern Commentary on early Chinese Mathematics, including roots and quadratics,1,0,

,11,0,0,0,0,0,Lienard,Chipart,,Sur le signe de la partie réelle des racines d'une équation algébrique,J. Math. Pures Appl. (Ser. 6),10,,,1914,291,346,Classical paper on stability (negative real part of roots),1,0,

,19,0,0,0,0,0,Enestrom, G.,,,no title,Bibl. Math. (Ser. 3),8,,,1907,184,185,refers to quadratics among the Arabs,1,0,

,29,0,0,0,0,0,Nagai, T.,Hatano, Y.,,Performance evalution of mathematical functions,Supercomputer,8,,,1991,46,56,Considers SQRT on vector computers,1,0,

,20,0,0,0,0,0,Ronveaux, A.,Belmehdi, S.,,Interlacing properties of the zeros of the derivative, associated and adjacent of semi-classical and classical orthogonal polynomials,Ann. Numer. Math.,2,,,1995,159,168,,1,0,

,20,21,0,0,0,0,Elbert, A.,Laforgia, A.,,On the zeros of associated polynomials of classical orthogonal polynomials,Differ. Integr. Eq.,6,,,1993,1137,1143,Also considers zeros of derivative polynomials,1,0,

,26,0,0,0,0,0,Winkler J.R.,,,Condition numbers of a nearly singular simple root of a polynomial,Appl Numer. Math.,38,,,2001,275,285,Condition number of 2 roots z₀ and z₀+ε (ε small),1,0,

,1,5,8,0,0,0,Cardelino C.A.,Chen P.Y.,,A new parallel algorithm for solving a complex function F(z)=0, in "Internat. Conf. On Parallel Processing",,,,,1985,305,0,Uses argument principle and 2-D bisection. Also downhill method,1,0,

,21,0,0,0,0,0,Pasquini L.,,,Computation of the zeros of orthogonal polynomials, in "Orthogonal Polynomials and their Applications", C. Brezinski et al (eds),,,J.C. Balzer,Basel,1991,359,364,,1,0,

,21,0,0,0,0,0,Ronveaux A.,,,Zeros of associate versus zeros of derivatives of classical orthogonal polynomials, in "Orthogonal Polynomials & their Applications, C. Brezinski et al (eds),,,J.C. Balzer,Basel,1991,419,0,,1,0,

,19,0,0,0,0,0,Biagio M.,,,Chasi exemplari alla regola dell'Algebre, nella trascelta a Cura di M. Benedetto,,,,Siena,1983,0,0,Medieval treatment of low degree polynomials,1,0,

,17,0,0,0,0,0,Kiper A.,,,Modified Dorn's algorithm with improved speed-up, in "Applied Parallel Computing: Industrial Computation and Optimization", LNCS 1184,,,Springer-Verlag,New York,1997,432,433,Algorithm within 1 time unit of optimality,1,0,

,17,0,0,0,0,0,Munro J.I.,Paterson M.,,Optimal algorithms for parallel polynomial evaluation,J. Comput. System Sci.,7,,,1973,189,198,Parallel version of Homer's method for evaluating polynomials,1,0,

,29,0,0,0,0,0,Neugebauer O.,,,Bemurkungen uber Quadratwurzeln und Quadratwurzel-Approximationen in der Babylonischen Mathematik,Quel. Stud. Gesch. Math.,B2,,,1932,291,296,Ancient square roots,1,0,

,29,0,0,0,0,0,Schulte M.,Swartzlander E.E.,,Exact Rounding of Certain Elementary Functions, in "11th Symp. On Comput. Arith.",,,,,1993,138,145,Treats square root.,1,0,

,3,0,0,0,0,0,Hopkins M.,Marshall B.,Schmidt G. & S. Zlobec,On a method of Weierstrass for the simultaneous calculation of the roots of a polynomial,Zeit. Angew. Math. Mech.,74,,,1994,295,306,Proves some results for Weierstrass' method,1,0,

,19,29,0,0,0,0,Gauchet L.,,,Note sur la generalisation de l'extraction de la racine carrée chez les anciens auteurs Chinois,T'Oung Pao,15,,,1914,531,550,,1,0,

,0,0,0,0,0,0,Slugin S.,,,Some applications of the method of two-sided approximation,Izv. Vys. Uch. Zav. Mat.,7,,,1958,244,256,,1,0,

,29,0,0,0,0,0,Nagai T.,Hatano Y.,,Performance evaluation of mathematical functions,Supercomputer,8, issue 6,,,1991,45,56,Treats SQRT on vector computers,1,0,

,19,0,0,0,0,0,Davis M.D.,,,Piero della Francesca's Mathematical treatises,,,Longo Editore,Ravenna,1977,0,0,Treats low -order polynomials,1,0,

,13,0,0,0,0,0,Ho P.Y.,,,Ch'in in Chiu-shao,Dict. Sci. Biog,3,,,1971,249,256,Horner's method described,1,0,

,13,0,0,0,0,0,Ho P.Y..,,,Chu Shih-chieh,Dict. Sci. Biog.,3,,,1971,265,271,Horner's method described,1,0,

,13,0,0,0,0,0,Ho P.Y.,,,Liu Hui,Dict. Sci. Biog.,8,,,1973,418,425,Horner's method described,1,0,

,13,0,0,0,0,0,Ho P.Y.,,,Li Chi,Dict. Sci. Biog.,8,,,1973,313,320,Horner's method described,1,0,

,3,0,0,0,0,0,Petkovic L,Trickovic S,,On the construction of simultaneous methods for multiple zeros,Nonlin. Anal. Theory Meth. Appl.,30,,,1997,669,676,Approximates f''/f'. Applies to multiple roots (multiplicity known),1,0,

,1,2,7,14,16,0,Yakowitz S,Szidarovszky F,,An introduction to numerical computations 2nd ed.,,,MacMillan,New York,1989,0,0,Treats Bisection, Newton, Secant, Bairstow, convergence,1,0,

,29,0,0,0,0,0,Garrett G.T. (ed),,,The Legacy of India,,,Oxford,,1937,0,0,Gives approximation to sqrt(2),1,0,

,21,0,0,0,0,0,Biehler C.,,,Sur les équations binomes,Nouv. Ann. Math. Ser. 3,9,,,1890,472,476,,1,0,

,21,0,0,0,0,0,Candido G.,,,Sulla risoluzione algebrica della equazione x^{p^k} ± 1= 0,Giorn. Mat.,46,,,1908,346,348,,1,0,

,4,0,0,0,0,0,von Sanden H.,,,Praktische Mathematik,,,Teubner,Stuttgart,1958,0,0,Treats Graeffe's method,1,0,

,1,2,7,16,24,0,Mathews J.H.,Fink K.D.,,Numerical Methods Using Matlab 3/E,,,Prentice Hall,,1999,0,0,Treats bisection, Newton, secant, Muller, convergence, acceleration,1,0,

,25,0,0,0,0,0,Abel N.H.,,,Memorial publie á l'occasion du centenaire de sa naissance,,,Gauthier-Villars,Paris,1902,0,0,Treats non-existence of solution by radicals for n>4,1,0,

,2,4,5,7,10,14,Korn G.A.,Korn T.M.,,Mathematical handbook for scientists and engineers 2nd ed.,,,McGraw-Hill,New York,1968,0,0,Treats briefly Newton, Graeffe, QD, Secant, Muller, Sturm, Baistow, bounds, evaluation, and a matrix method,1,0,

,11,14,18,19,24,,Korganoff A.,,,Méthodes de Calcul Numérique Vol 1,,,Dunod,Paris,1961,0,0,Describes nearly all the classical methods including Aitken.,1,0,

,25,0,0,0,0,0,Postnikov N.H.,,,Foundations of Galois Theory Trans. A. Swinfen,,,Pergamon,Oxford,1962,0,0,Considers solvability by radicals (and non-solvability) for n>4.,1,0,

,11,0,0,0,0,0,Balinskii A.I.,Podlevskii B.M.,,The relationships between the methods of Hermite, Schur, and Lyapunov in the stability theory of polynomials,Comput. Math. Math. Phys.,42,,,2002,1235,1241,Title says it,1,0,

,18,0,0,0,0,0,Linden H.,,,Containment regions for zeros of polynomials from numerical ranges of companion matrices,Lin. Alg. Appl.,350,,,2002,125,145,A priori bounds on roots,1,0,

,7,0,0,0,0,0,Routledge N.,,,More on iterative solutions of F(x)=0,Math. Gaz.,86,,,2002,481,484,Treats reguli falsi, including rate of convergence.,1,0,

,19,0,0,0,0,0,Holmes G.C.,,,The use of hyperbolic cosines in solving cubic polynomials,Math. Gaz.,86,,,2002,473,477,Mainly case of only one real root of cubic,1,0,

,21,0,0,0,0,0,Krasovsky I.V.,,,Asymptotic distribution of zeros of polynomials satisfying difference equations,J. Comput. Appl. Math.,150,,,2003,57,70,Treats Meixner polynomials,1,0,

,19,0,0,0,0,0,Lockhart J.,,,Resolution of Cubic Equations,,,,Harlem,1825,0,0,,1,0,

,21,0,0,0,0,0,Gatteschi L.,,,Asymptotics and bounds for the zeros of Laguerre polynomials: a survey,J. Comput. Appl. Math.,144,,,2002,7,28,,1,0,

,19,22,25,0,0,0,Scherk J.,,,Algebra: a Computational Introduction,,,Chapman & Hall,,2000,0,0,Treats cubics, quartics, finite fields, existence & solution by radicals,1,0,

,15,0,0,0,0,0,He J.-H.,,,A new iteration method for solving algebraic equations,Appl. Math. Comput.,135,,,2003,81,84,uses 2nd derivative. Claims "high convergence" but does not state order.,1,0,

,1,2,17,0,0,0,Murphy J,Ridout D,McShane B,Numerical Analysis, Algorithms and Computation,,,Halsted Press,New York,1988,0,0,Treats bisection, Newton, and evaluation,1,0,

,1,2,7,24,0,0,Pearson C.E.,,,Numerical Methods in Engineering and Science,,,Van Nostrand Reinhold,New York,1986,0,0,Treats bisection, Newton, Secant, and acceleration,1,0,

,1,2,0,0,0,0,Constabile F et al,,,An iterative method for the computation of solutions of non-linear equations,Calcolo,36,,,1999,17,34,Combines assured convergance of bisection with speed of Newton-like method. Works better than Newton.,1,0,

,2,4,6,7,14,18,Rektorys K (ed),,,Survey of Applicable Mathematics,,,MIT Press,Cambridge, Mass.,1969,1169,0,Treats Newton, Graeffe, QD, Secant, Bairstow, Sturm and bounds. Medium level of detail.,1,0,

,11,0,0,0,0,0,Bhattacharyya S. P.,,,Robust stabilization against structured perturbations,Lecture Notes in Contr. And Infor. Sci.,99,Springer-Verlag,,1987,0,0,Proves Kharitonov's Theorem, etc.,1,0,

,2,7,0,0,0,0,Weeg G.P.,Reed G.B.,,Introduction to Numerical Analysis,,,Blaisdell,Waltham, Mass.,1966,0,0,Treats Newton, Reguli Falsi,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,A generalization of Kharitonov's four polynomial concept for robust stability problems with linearly dependant coefficient perturbations,IEEE Trans. Automat. Control,34,,,1989,157,165,,1,0,

,11,0,0,0,0,0,Barmish B.R.,DeMarco C.L.,,Criteria for robust stability of systems with structured uncertainty: a perspective,Proc. Amer. Contr. Conf.,,,Minneapolis, MN,1987,476,481,,1,0,

,29,0,0,0,0,0,Datta B,,,The Bakhshali Mathematics,Bull. Calcutta Math. Soc.,21,,,1929,1,60,Hindu square root,1,0,

,19,0,0,0,0,0,Loria G,,,Leonardo Fibonacci in "Gli scienziati italiani" ed A. Mieli,,,,Rome,1923,4,12,Brief treatment of particular quadratics,1,0,

,19,0,0,0,0,0,Woepke F,,,Sur un essai de déterminer la nature de la racine d'une équation du troisième degré, contenue dans un ouvrage de Léonard de Pise,J. Math. Pures Appl.,19,,,1854,401,406,Early cubic,1,0,

,11,0,0,0,0,0,Vicino A,,,Some results on robust stability of discrete time systems,IEEE Trans. Automat. Control,33,,,1988,844,847,,1,0,

,19,0,0,0,0,0,Hoyrup J.,,,Sub-scientific mathematics: observations on a pre-modern phenomenon.,Hist. Sci.,28-1 (79),,,1990,63,87,Brief quadratics.,1,0,

,19,29,0,0,0,0,Chang F.-J.,,,Les Fonctionnaires des Song, Index des Titres.,,,Mouton,Paris,1962,0,0,Chinese treatment of roots and low-degree equations.,1,0,

,13,0,0,0,0,0,Grattan-Guinness I. (ed),,,Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. (2 volumes),,,Routledge,London,1994,0,0,Brief history of equations.,1,0,

,1,2,10,0,0,0,Rojas J.M.,Ye Y.,,On solving univariate sparse polynomials in logarithmic time.,J. Complexity,21,,,2005,87,110,Considers case of only 3 non-zero terms.,1,0,

,29,0,0,0,0,0,Hernandez M.A.,Romero N.,,Accelerated convergence in Newton's method for approximating square roots.,J. Comput. Appl. Math.,177,,,2005,225,229,Title says it.,1,0,

,3,0,0,0,0,0,Petkovic L.D.,Petkovic M.S.,Zivkovic D.,Hansen-Patrick's family of Laguerre's type.,Novi. Sad. J. Math.,33,,,2003,109,115,Studies cubically convergant methods. Hansen-Patrick follows from Laguerre.,1,0,

,19,25,0,0,0,0,Grattan-Guinness I.,,,The Norton History of the Mathematical Sciences.,,,W.W. Norton & Co.,New York,1997,0,0,Quadratics, existence, solutions by radicals.,1,0,

,19,0,0,0,0,0,Rigatelli T.,,,Towards a history of algebra from Leonardo of Pisa to Luca Pacioli.,Janus,72,,,1985,17,82,Numerical solution of cubic, etc.,1,0,

,19,29,0,0,0,0,Franci R.,Rigatelli L.T.,,Maestro Benedetto de Firenze e la Storia dell'Algebra.,Hist. Math.,10,,,1983,297,317,Early quadratics and roots.,1,0,

,19,0,0,0,0,0,Hughes B.,,,The medieval Latin translations of al-Khwarizmi's Al'Jabr.,Manuscripta,26,,,1982,31,37,Brief treatment of quadratics among Arabs.,1,0,

,19,0,0,0,0,0,Sédillot L.A.,,,De l'algèbre chez les Arabs,J. Asiatique 5th ser.,2,,,1853,323,350,Geometric treatment of cubic.,1,0,

,19,0,0,0,0,0,Thureau-Dangin F.,,,Textes Mathématiques Babyloniens.,,,Leiden,,1938,0,0,Very early treatment of quadratic.,1,0,

,2,7,17,1,15,9,Engeln-Müllges G.,Uhlig F.,,Numerical Algorithms with C.,,,Springer-Verlag,Berlin,1996,0,0,Treats Newton, bisection, reguli falsi, Muller, Horner, Jenkins-Traub, Laguerre.,1,0,

,7,15,0,0,0,0,Press W.H.,Flannery B.P.,Teukolsky S.A. et al,Numerical Methods in Fortran 90- the Art of Parallel Scientific Computing.,,,Cambridge U.P.,Cambridge,1996,0,0,Gives programs for several standard methods.,1,0,

,2,0,0,0,0,0,Kelley C.T.,,,Iterative Methods for Linear and Nonlinear equations.,,,SIAM Press,Philadelphia,1995,0,0,Modifies Newton.,1,0,

,3,0,0,0,0,0,Petkovic M.S.,Ilic S.,Rancic L.,The convergence of a family of parallel zero-finding methods.,Computetrs Math. Applic,48,,,2004,455,467,Gives conditions for convergence of some 4th-order methods.,1,0,

,19,0,0,0,0,0,Curtze M.,,,Petri Philomeni de Dacia in Algorisum Vulgarum Johannis de Sacrobosco Commentarius una cum Algorismo ipso.,,,,Copenhagen,1987,0,0,Early quadratic.,1,0,

,10,0,0,0,0,0,Hong H.,,,Ore Subresultant Coefficients in Solutions,Applic. Alg. Eng. Comm. Comput.,12,,,2001,421,428,No note.,1,0,

,29,0,0,0,0,0,Martzloff J.-C.,,,Recherches sur l'Oeuvre Mathématique de Mei Wending (1633-1721),Mem. Inst. Hau. Etd. Chinioses,16,College de France,Paris,1982,0,0,n'th roots in early China.,1,0,

,19,29,0,0,0,0,Rashed R.,,,The development of Arabic mathematics: between arithmetic and algebra. Trans. A.F.W. Armstrong.,,,Kluwer,Boston,1994,0,0,Surds and low-degree among Arabs.,1,0,

,20,0,0,0,0,0,Bonorden O.,von zur Gathen J.,Gerhard J. et al,Factoring a binary polynomial of degree over one million.,SIGSAM Bull.,35-1,,,2001,16,18,Title says it.,1,0,

,20,0,0,0,0,0,Flajolet P.,Gourdon X.,Panario D.,The complete analysis of a polynomial factorization algorithm over finite fields.,J. Algorithms,40-1,,,2001,37,81,No note.,1,0,

,20,0,0,0,0,0,van Hoeij M.,,,Factoring polynomials and the knapsack problem.,J. Number Theory,95,,,2002,167,189,New algorithm much faster than Berlekamp-Zassenhaus.,1,0,

,20,0,0,0,0,0,Lenstra H.W. Jr.,,,"Finding small degree factors of lacunary polynomials" in Number Theory in Progress, Walter de Gruyter.,,1,,,1999,267,276,No note.,1,0,

,20,0,0,0,0,0,Lenstra H.W. Jr.,,,"On the factorization of lacunary polynomials" in Number Theory in Progress, Walter de Gruyter.,,1,,,1999,277,291,No note.,1,0,

,15,0,0,0,0,0,Petkovic M.S.,Herceg D.,,On the rediscovered iteration methods for solving equations.,J. Comput. Appl. Math.,107,,,1999,275,284,Uses high-order derivatives.,1,0,

,30,0,0,0,0,0,Fiedler M.,,,Expressing a polynomial as the characteristic polynomial of a symmetric matrix.,Linear Algebra Appl.,141,,,1990,265,270,Title says it.,1,0,

,19,0,0,0,0,0,Tong J.,,,b²-4ac and b²-3ac,Math. Gaz.,88,,,2004,511,513,Uses b²-4ac and some functions of it to find number of real roots of a cubic,1,0,

,25,0,0,0,0,0,de Sousa J.C.,Santos O.,,Another Proof of the Fundamental Theorem of Algebra,Amer. Math. Monthly,112,,,2005,76,78,Short proof of existence,1,0,

,28,0,0,0,0,0,Romik D.,,,Roots of the Derivative of a Polynomial,Amer. Math. Monthly,112,,,2005,66,69,Refers to a very special (Wilkinson) polynomial,1,0,

,19,0,0,0,0,0,Hughes, B.,,,Gerard of Cremona's translation of al-Kharizmi's Al-Jabr: A critical edition,Mediaeval Studies,48,,,1986,211,263,Arabic quadratics,1,0,

,20,0,0,0,0,0,Insua M.A.,Ladra M.,,A note on Grobner bases and Berlekamp's algorithm,Appl. Math. Comput.,196,,,2008,77,85,Factorizes over finite fields,1,0,

,15,0,0,0,0,0,Ide N.,,,A new hybrid iteration method for solving algebraic equations,Appl. Math. Comput.,195,,,2008,772,774,Uses 2nd derivative. No convergence analysis,1,0,

,2,0,0,0,0,0,Thukral R.,,,Introduction to a Newton-type method for solving nonlinear equations,Appl. Math. Comput.,195,,,2008,663,668,Generalized Newton; 3rd order with 3 evaluations.,1,0,

,15,0,0,0,0,0,Han D.,Wu P.,,A family of combined iterative methods for solving nonlinear equations,Appl. Math. Comput.,195,,,2008,448,453,Composes Newton and higher order methods,1,0,

,15,0,0,0,0,0,Jiang D.,Han D.,,Some one-paramater families of third-order methods for solving nonlinear equations,Appl. Math. Comput.,195,,,2008,392,396,Some well-known 3rd order methods using 3 evaluations are special cases,1,0,

,10,0,0,0,0,0,Tsigaridis E.P.,Emiris I.Z.,,On the complexity of real root isolation using continued fractions,Theor. Comp. Sci.,392,,,2008,158,173,0(n ³b ) where n=degree and b=number of bits,1,0,

,28,0,0,0,0,0,Bray H.,,,On the zeros of a polynomial and its derivatives,Amer. J. Math.,53,,,1931,864,872,,1,0,

,15,0,0,0,0,0,Amat S.,Busquier S.,Plaza S.,Dynamics of a family of third-order iterative methods that do not require using second derivatives,Appl. Math. Comput.,154,,,2004,735,746,,1,0,

,19,0,0,0,0,0,Hayashi T.,,,Sridhara's authorship of the mathematical treatise Ganita pancavimst,Hist. Scient. (2),4,,,1995,233,250,Quadratics in early India,1,0,

,19,25,10,11,2,7,Delone B.N.,,,Algebra: Theory of algebraic equations, in "Math.: It's content, methods and meaning" ed Aleksandrov et al,,,MIT Press,Cambridge, MA,1956,261,310,Existence, Sturm sequences, stability, Newton, secant, Graeffe,1,0,

,31,0,0,0,0,0,Corless R.M.,Giesbrecht M.W.,Jeffrey D.J. & Watt S.M.,Approximate Polynomial Decomposition, in ISSAC99,,,ACM Press,New York,1999,213,219,Uses series,1,0,

,15,0,0,0,0,0,Ezquerro J.A.,Hernandez M.A.,,On a convex acceleration of Newton's method,J. Optim. Theory Appl.,100,,,1999,311,326,Uses 2nd derivative,1,0,

,15,0,0,0,0,0,Buff X.,Henriksen C.,,On Konig's root-finding algorithms,Nonlinearity,16,,,2003,989,1015,Uses higher derivatives,1,0,

,17,0,0,0,0,0,Gemignani L.,,,A generalized Graeffe's iteration for evaluating polynomials and rational functions, in ISSAC 01,,,ACM Press,New York,2001,143,149,Evaluates a polynomial at the roots of another,1,0,

,19,0,0,0,0,0,Buckley J.J.,,,Solving fuzzy equations,Fuzzy Sets Sys.,50,,,1992,1,14,Treats fuzzy quadratic,1,0,

,18,0,0,0,0,0,Schmeisser G.,,,Estimates for the imaginary parts of the zeros of a polynomial,Math. Balkanica New Ser.,16,,,2002,203,217,Gives bounds for imaginary part of zero,1,0,

,13,0,0,0,0,0,Gonzalez Vega L.,Lombardi H.,Mahe L.,Virtual roots of real polynomials,J. Pure Appl. Algebra,124,,,1998,147,166,,1,0,

,11,0,0,0,0,0,Polyak B.T.,Tsypkin Ya Z.,,Comments on two necessary conditions for a complex polynomial to be strictly Hurwitz and their applicaations in robust stability analysis,IEEE Trans. Autom. Contr.,39,,,1994,1147,1148,,1,0,

,11,0,0,0,0,0,Padmanabhan P.,Holot C.V,,Complete instability of a box of polynomials,IEEE Trans. Autom Contr.,37,8,,,1992,1230,1233,,1,0,

,10,0,0,0,0,0,Wang D.,,,Subresultants with the Bezout matrix in Computer Mathematics,Proc. 4th Asian Symp Comp. Math.ASCM2000,,World Scientific,,2000,19,28,,1,0,

,25,0,0,0,0,0,Wood J.,,,On the roots of equations,Phil.Trans.Roy. Soc. Lond.,88,,,1798,368,377,Existence,1,0,

,25,0,0,0,0,0,Von Staudt C.,,,Beweis des Satzes, dass jede algebraische rationale ganze Function von einer Verlanderlichen in Factoren vom ersten Grade aufgelost werden kann,J. Reine Angew Math.,29,,,1845,97,103,Existence,1,0,

,25,0,0,0,0,0,Malet J.C.,,,Proof that every algebraic equation has a root,Trans. Roy. Irish. Acad.,26,,,1878,453,455,Existence,1,0,

,16,0,0,0,0,0,Kacewicz B.,Wozniakowski H.,,A survey of recent problems and results in analytic computational complexity in 'Mathematical Foundations of Computer Science 77', J. Gruska ed.,,,Springer Verlag,Berlin, London,1977,83,107,Gives bounds on order of convergence of various classes of methods,1,0,

,3,0,0,0,0,0,Zheng S.,,,On convergence of Durand-Kerner's method for finding all roots of polynomial simultaneously,Kexue Tongbao,27,,,1982,1262,1265,Title says it,1,0,

,3,0,0,0,0,0,Batra P.J.,,,Improvement of a convergence condition for the Durand-Kerner iteration,J. Comput. Appl. Math.,96,,,1998,117,125,Title says it,1,0,

,13,0,0,0,0,0,Chen W.,,,On the polynomials with all their zeros on the unit circle,J. Math. Anal. Appl.,190,,,1995,714,724,Shows conditions for zeros to lie on unit circle,1,0,

,4,,,,,,Delone B.N.,,,Algebra: Theory of algebraic equations, in "Math.: It's content, methods and meaning" ed Aleksandrov et al,,,MIT Press,Cambridge, MA,1956,261,310,Existence, Sturm sequences, stability, Newton, secant, Graeffe,1,0,

,2,15,0,0,0,0,Kanwar V.,Singh S.,Bakshi S.,Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations,Numer. Algor.,47,,,2008,95,107,Family of mostly third order methods,1,0,

,19,0,0,0,0,0,Hawthorne F.,,,Completing the square,Math. Stud. J.,39(1),,,1956,1,1,,1,0,

,19,0,0,0,0,0,Sharman H.L.,,,The quadratic equation,Math. Gaz.,27,,,1943,184,185,Proof of expression for roots of quadratic,1,0,

s2gj35,21,,,,,,Greenwood R.E.,Danford M.B.,,Numerical integration with a weight function x,J. Math. and Phys.,28,,,1949,99,106,,1,,

s2gj36,10,,,,,,Grunert J.A.,,,Beweis des Harriotischen Satzes,J. Reine Angew. Math.,2,,,1827,335,344,,1,,

s2gj37,13,,,,,,Grunert J.A.,,,Die Methoden von Tschirnhaus und Jerrard zur Transformation der Gleichungen,Arch. Math. Phys.,40,,,,214,231,,1,,

s2gj38,10,,,,,,Guidice F.,,,Sulla determinazione delle radici reali d'equazione a coefficienti numerici reali,Rend. Circ. Mat. Palermo,1,,,1884,69,72,,1,,

s2gj39,10,,,,,,Guidice F.,,,Separazione delle radici reali d'equazione a coefficienti numerici reali,Giorn. Mat.,41,,,1903,190,191,,1,,

s2gj40,13,,,,,,Guidice F.,,,Existenza calcolo e differenze di radici d'equazioni numeriche,Rend. Circ. Mat. Palermo,14,,,1902,180,184,,1,,

s2gj41,31,,,,,,Guidice F.,,,Sul calcolo assintotico delle radici reali d'equazione,Giorn. Mat.,41,,,1903,14,20,,1,,

s2gj42,10,,,,,,Guilmin,,,Conséquences de la règle des signes de Descartes,Nouv. Ann. Math.,5,,,1846,239,244,,1,,

s2gj43,13,,,,,,Günther S.,,,Ueber die allgemeine Auflösung von Gleichungen durch Kettenbrüche,Math. Ann.,7,,,1874,262,268,,1,,

s2gj44,21,,,,,,Günther S.,,,Eine didaktisch wichtige Auflösung trinomischer Gleichungen,Zeit. Math. Naturwiss. Unterricht,11,,,1880,68,72,,1,,

s2gj44,21,,,,,,Günther S.,,,Eine didaktisch wichtige Auflösung trinomischer Gleichungen,Zeit. Math. Naturwiss. Unterricht,11,,,1880,267,267,,1,,

s2gj45,29,,,,,,Günther S.,,,Die Quadratischen Irrationalitälen der Alten und deren Entiwickelungsmethoden,Abhandlungen Zur Geschichte der Mathematik,4,,,1882,83,86,,1,,

s2cb32,28,,,,,,Coppersmith D.,Neff C.A.,,Roots of a Polynomial and its Derivatives in "Fifth Annual ACM-SIAM Symposium on Discrete Algorithms",,,,,1994,271,279,,1,,

s2dj12,19,,,,,,Demongeot A.,,,Sur la résolution des équations du troisième degré au moyen des tables trigonométriques,Nouv. Ann. Math.,20,,,1861,143,147,,1,,

s2dj13,13,,,,,,de Morgan A.,,,Remark on Horner's method of solving equations,The Mathematician,3,,,1851,289,291,,1,,

s2dj14,2,19,,,,,Dence T.,,,Cubics; chaos; and Newton's method,Math. Gaz.,81,,,1997,403,408,,1,,

s2dj15,29,,,,,,Destefanis M.,,,Estrazione della radice quadrata,Atti Accad. Sci. Torino,54,,,1918,89,96,,1,,

s2dj16,18,,,,,,Deutsch E.,,,The smallest zero of a polynomial; in Problems and Solutions,Amer. Math. Monthly,78,,,1971,799,799,,1,,

s2dj17,29,,,,,,Devries R.C.,Chao M.H.,,Fully iterative array for extracting square roots,Electron. Lett.,6,,,1970,255,256,,1,,

s2dj18,18,,,,,,Dewan K.K.,,,On the location of zeros of polynomials,Math. Student; Madras,50,,,1982,170,175,,1,,

s2dj19,20,,,,,,Dickson L.E.,,,On higher congruences and modular invariants,Bull. Amer. Math. Soc.,14,,,1907,313,318,,1,,

s2dj20,19,20,,,,,Dickson L.E.,,,Note on cubic equations and congruences,Ann. Math. Ser. 2,12,,,1911,149,152,,1,,

s2dj21,31,,,,,,Dietrich R.,,,Ueber die Darstellung der Wurzeln der algebraischen Gleichungen durch unendliche Reihen,Arch. Math. Phys.,69,,,1883,337,380,,1,,

s2dj22,28,,,,,,Dimitrov D.,,,On a conjecture of Sendov,C.R. Acad. Bulgare Sci.,36,,,1983,561,563,,1,,

s2dj23,3,,,,,,Dochev K.,,,über Newtonsche Iterationen,C.R. Acad. Bulgare Sci.,15,,,1962,695,701,,1,,

s2dj24,10,,,,,,Dornstetter J.L.,,,On the equivalence between Berlekamp's and Euclid's algorithms,IEEE Trans. Inform. Theory,33,,,1987,428,431,,1,,

s2dj25,19,,,,,,Dörrie H.,,,Die numerische Auflösung kubischer... Gleichungen,Arch. Math. Phys. Ser. 3,11,,,1907,168,173,,1,,

s2dj26,19,25,,,,,Doyle P.,McMullen C.,,Solving the quintic by iteration,Acta Math.,163,,,1989,151,180,,1,,

s2dj27,15,,,,,,Du Q. et al,,,The Quasi-Laguerre Iteration,Math. Comp.,66,,,1997,345,361,,1,,

s2dj28,29,,,,,,Dubeau F.,,,Algorithms for the n'th Root Approximation,Computing,57,,,1996,365,369,,1,,

s2dj29,29,,,,,,Dubeau F.,,,Nth Root extraction: Double iteration process and Newton's method,J. Comput. Appl. Math.,91,,,1998,191,198,,1,,

s2gb25,29,,,,,,Gosling J.B.,,,"Design of Arithmetic Units for Digital Computers",,,MacMillan,London,1980,125,126,,1,,

s2gb26,29,,,,,,Gow J.,,,"A short History of Greek mathematics",,,,Cambridge,1884,,,,1,,

s2gb27,20,,,,,,Grigoriev D. Yu.,,,Computational complexity in polynomial algebra in "Proc. Intern. Congress of Mathematicians",,,,,1987,1452,1460,,1,,

s2gb28,2,6,13,19,29,,Günther S.,Wieleitner H.,,"Geschichte der Mathematik I/II",,,,Leipzig,1908,,,,1,,

s2hj1,31,,,,,,Hagen J.G.,,,On the Reversion of Series and its Application to the Solution of Numerical Equations,Proc. Amer. Phil. Soc.,21,,,1883,93,101,,1,,

s2hj2,19,,,,,,Halley E.,,,De constructione problematum solidorum; sive aequationum tertiae vel quartae potestatis; unica data parabola ac circulo,Philos. Trans. Roy. Soc. London,16,,,1687,376,381,,1,,

s2hj3,19,,,,,,Halphen G.H.,,,Formules d'Algèbre. Résolution des équations du troisième et du quatrième degré,Nouv. Ann. Math. Ser. 2,4,,,1885,17,35,,1,,

s2hj4,21,,,,,,Han S.S.,Kwon K.H.,Littlejohn L.L.,Zeros of orthogonal polynomials in certain discrete Sobolev spaces,J. Comput. Appl. Math.,67,,,1996,309,325,,1,,

s2hj5,20,,,,,,Han W.B.,,,Primitve Roots and Linearized Polynomials,Advances in Mathematics (China),22,,,1993,460,462,,1,,

s2hj6,20,,,,,,Han W.B.,,,The coefficients of the primitive polynomials over finite fields,Math. Comp.,65,,,1996,331,340,,1,,

s2hj7,17,,,,,,Hansen E.R.,,,Global optimization using interval analysis: the one-dimensional case,J. Optimization Theory and Applications,29,,,1979,331,344,,1,,

s2hj8,12,,,,,,Hansen E.R.,,,Computing Zeros of Functions using Generalized Interval Arithmetic,Interval Computations (Russia),3,,,1993,1,28,,1,,

s2hj9,2,12,,,,,Hansen E.R.,Walster G.W.,,Nonlinear equations and Optimization,Comput. Math. Appl.,25 No. 10/11,,,1993,125,145,,1,,

s2hj10,19,,,,,,Harley R.,,,On the theory of the transcendental Solution of algebraic equations,Quart. J. Math.,5,,,1862,337,360,,1,,

s2hj11,4,,,,,,Hasan M.A.,Hasan A.A.,,Hankel Matrices and Their Applications to the Numerical Factorization of Polynomials,J. Math. Anal. Appl.,197,,,1996,459,488,,1,,

s2hj12,10,,,,,,Hasan M.A.,Hasan A.A.,,Hankel Matrices of Finite Rank with Applications to Signal Processing and Polynomials,J. Math. Anal. Appl.,208,,,1997,218,242,,1,,

s2hj13,29,,,,,,Hashemian R.,,,Square rooting algorithms for integer and floating point numbers,IEEE Trans. Comput.,39,,,1990,1025,1029,,1,,

s2hj14,20,,,,,,Hasse H.,,,Zwei Bemerkungen zu der Arbeit von U. Wegner,Math. Ann.,106,,,1932,455,456,,1,,

s2hj15,19,,,,,,Hausner A.,,,The Bring-Jerrard Equation and Weierstrass Elliptic Functions,Amer. Math. Monthly,69,,,1962,193,196,,1,,

s2hj16,19,,,,,,Hayashi T.,,,A Brief History of the Japanese Mathematics,Nieuw Archief voor Wiskunde; Ser. 2,6,,,1904,296,361,,1,,

s2hj17,21,,,,,,He M.,Pan K.,Ricci P.E.,Asymptotics of the zeros of relativistic Hermite polynomials,SIAM J. Math. Anal.,28,,,1997,1248,1257,,1,,

s2hj18,19,25,,,,,Head A.K.,,,The Galois unsolvability of the sextic equation of anisotropic elasticity,J. Elasticity,9,,,1979,9,20,,1,,

s2hj19,19,,,,,,Heilermann,,,Bemerkung zu der Auflösung der biquadratischen Gleichungen,Z. Math. Phys.,21,,,1876,364,365,,1,,

s2hj20,19,,,,,,Hellins J.,,,A new Method of Finding the Equal Roots of an Equation by Division,Philos Trans. Roy. Soc. London,72,,,1782,417,425,,1,,

s2hj21,13,,,,,,Helmke U.,Fuhrmann P.A.,,Bézoutiants,Lin. Algebra Appl.,124,,,1989,1039,1097,,1,,

s2hj22,10,,,,,,Hensel K.,,,Neue Grundlagen der Arithmetik,J. Reine Angew. Math.,127,,,1904,51,84,,1,,

s2hj23,20,,,,,,Hensel K.,,,über die zu einer algebraischen Gleichung gehörigen Auflösungskörper,J. Reine Angew. Math.,136,,,1909,183,209,,1,,

s2hj24,19,,,,,,Hermann A.,,,Sur le cas irréductible de l'équation du troisième degré,Nouv. Ann. Math. Ser. 2,6,,,1867,270,275,,1,,

s2hj25,19,,,,,,Hermite C.,Jerrard,,Die Transformation und Auflösung der Gleichungen fünften Grades,Z. Math. Phys.,4,,,1859,77,96,,1,,

s2hj26,15,,,,,,Hernándes M.A.,Salanova M.A.,,Chebyshev method and convexity,Appl. Math. Comput.,95,,,1998,51,62,,1,,

s2hj27,13,16,,,,,Hertling P.,,,Topological Complexity with Continuous Operations,J. Complexity,12,,,1996,315,338,,1,,

s2hj28,16,,,,,,Herzberger J.,,,Untere Schranken für die positiven Wurzeln von Polynomen bei der Berechnung der R-Ordnung von Iterationsverfahren,Z. Angew. Math. Mech.,75 Supp.,,,1995,639,640,,1,,

s2hj29,3,7,15,,,,Herzberger J.,Metzner L.,,On the Q-Order of Convergence for Coupled Sequences Arising in Iterative Numerical Processes,Computing,57,,,1996,357,363,,1,,

s2hj30,10,13,,,,,Hesse O.,,,über die Bildung der Endgleichung; welche durch Elimination...,J. Reine Angew. Math.,27,,,1844,1,5,,1,,

s2hj31,31,,,,,,Heymann W.,,,Ueber die Auflösung der allgemeinen trinomischen Gleichung tⁿ+at^n-s+b=0,Z. Math. Phys.,31,,,1886,223,240,,1,,

s2hj32,19,,,,,,Heyman W.,,,Theorie der trinomische Gleichungen,Math. Ann.,28,,,1887,61,80,,1,,

s2hj33,13,,,,,,Hibbert L.,,,Résolution des équations algébriques de la forme zⁿ = z-a,C.R. Acad. Sci. Paris,206,,,1938,229,231,,1,,

s2hj34,13,,,,,,Hibbert L.,,,Cellules d'univalence des polynomes,C.R. Acad. Sci. Paris,205,,,1938,1121,1123,,1,,

s2hj35,19,,,,,,Hibbert L.,,,Résolution des équations zⁿ = z-a,Bull. Sci. Math.,63,,,1941,21,50,,1,,

s2hj36,20,,,,,,Hidber C.,,,A Generalization of the Cantor-Zassenhaus Algorithm,Computing,59,,,1997,325,330,,1,,

s2hj37,29,,,,,,Hill,,,De radici cubica celeriter extrahenda,J. Reine Angew. Math.,11,,,1834,262,263,,1,,

s2hj38,29,,,,,,Hill,,,Méthode Rapide d'Approximation de la Racine Cubique,Nouv. Ann. Math.,7,,,1848,459,459,,1,,

s2hj39,2,,,,,,Hirst K.,,,Newton's method-with mistakes,Math. Gaz.,80,,,1996,385,389,,1,,

s2hj40,25,,,,,,Hölder O.,,,Zurüchführung einer beliebigen algebraischen Gleichung auf eine Kette von Gleichungen,Math. Ann.,34,,,1889,26,56,,1,,

s2hj41,17,,,,,,Hong H.,Stahl V.,,Bernstein Form is Inclusion Monotone,Computing,55,,,1995,43,53,,1,,

s2hj42,2,31,,,,,Horner J.,,,Approximation to the roots of algebraic equations in a series of aliquot parts,Quart. J. Pure Appl. Math.,3,,,1860,251,262,,1,,

s2hj43,2,,,,,,Housel,,,Méthode de M. Cauchy pour modifier la méthode de Newton dans la résolution des équations,Nouv. Ann. Math.,15,,,1856,244,256,,1,,

s2hj44,20,,,,,,Huang M.D.A.,,,Factorization of polynomials over finite fields and decomposition of primes in algebraic number fields,J. Algorithms,12,,,1991,482,489,,1,,

s2hj45,20,,,,,,Huang X.,Pan V.Y.,,Fast Rectangular Matrix Multiplication and Applications,J. Complexity,14,,,1998,257,299,,1,,

s2hj46,3,15,,,,,Huang Z.,Zheng S.,,On a family of parallel root-finding methods for generalized polynomials,Appl. Math. Comput.,91,,,1998,221,231,,1,,

s2hj47,20,,,,,,Huber K.,,,Solving equations in finite fields and some results concerning the structure of GF(pⁿ),IEEE Trans. Inform. Theory,12,,,1992,1154,1162,,1,,

s2hj48,5,,,,,,Hujter M.,,,Improving a Method of Search for Solving Polynomial Equations,Comput. Math. Appl.,31 (4/5),,,1996,187,189,,1,,

s2hj49,3,,,,,,Hull T.E.,Mathon R.,,The Mathematical Basis and a Prototype Implementation of a New Polynomial Rootfinder with Quadratic Convergence,ACM Trans. Math. Software,22,,,1996,261,280,,1,,

s2hj50,19,,,,,,Hurley A.C.,Head A.K.,,Explicit Galois Resolvents for Sextic Equations,Int. J. Quant. Chem.,31,,,1987,345,359,,1,,

s2hj51,11,,,,,,Hurwitz A.,,,Uber die Bedingungen unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besizst,Math. Ann.,46,,,1895,273,284,,1,,

s2hj52,20,,,,,,Hurwitz A.,,,über höherer Kongruenzen,Arch. Math. Phys. Ser. 3,5,,,1903,17,27,,1,,

s2hb1,25,,,,,,Hadlock C.R.,,,"Field Theory and its Classical Problems",,,Math. Ass. America,,1978,,,,1,,

s2hb2,13,,,,,,Hamilton W.R.,,,Inquiry into the validity of a method recently proposed by George B. Jerrard Esq. for transforming and resolving equations of elevated degrees in "British Assoc. for the Advancement of Science Report",,,,,1836,295,348,,1,,

s2hb3,12,17,30,,,,Hammer R. et al,,,"C++ Toolbox for Verified Scientific Computing I",,,Springer-Verlag,Berlin,1995,,,,1,,

s2hb4,19,,,,,,Hankel H.,,,"Zur Geschichte der Mathematik im Altertum und Mittelalter",,,,Leipzig,1874,,,,1,,

s2hb5,21,2,,,,,Hansen E.R.,,,A generalized interval arithmetic in "Interval Mathematics" Ed. K. Nickel,,,Springer-Verlag,New York,1975,7,18,,1,,

s2hb6,2,12,,,,,Hansen E.R.,,,"Global Optimization Using Interval Analysis",,,Marcel Dekker,New York,1992,,,,1,,

s2hb7,20,,,,,,Hardy G.H.,Wright E.M.,,"An Introduction to the Theory of Numbers 4/E",,,,Oxford,1960,,,,1,,

s2hb8,2,25,,,,,Haupt O.,,,"Einführung in die Algebra; Vol. II",,,Geest and Portig,Leipzig,1954,,,,1,,

s2hb9,29,,,,,,Heath T.L.,,,"The works of Archimedes",,,,Cambridge,1897,74,96,,1,,

s2hb10,19,,,,,,Heath T.L.,,,"History of Greek Mathematics Vol. 1",,,,Oxford,1921,151,379,,1,,

s2hb11,29,,,,,,Heath T.L.,,,"History of Greek Mathematics Vol. 2",,,,Oxford,1921,51,324,,1,,

s2hb12,19,29,,,,,Heath T.L.,,,"A Manual of Greek Mathematics",,,,Oxford,1931,,,,1,,

s2hb13,19,,,,,,Heath T.L.,,,"Diophantus of Alexandria 2/E",,,,New York,1964,,,,1,,

s2hb14,31,,,,,,Heegman A.,,,"Essai d'une nouvelle méthode de résolution des équations algébriques au moyen des séries infinies",,,Mallet-Bachelier,Paris,1861,,,,1,,

s2hb15,13,,,,,,Heegman A.,,,"Résolution Générale des équations",,,Gauthier-Villars,Paris,1865,,,,1,,

s2hb16,19,,,,,,Hermite C.,,,"Sur la Théorie des équations Modulaires et la Résolution de léquation du Cinquième Degré,,,Mallet-Bachelier,Paris,1859,,,,1,,

s2hb17,15,,,,,,Hermite C.,,,Sur un memoire de Laguerre concernant equations algebriques in "Oeuvres de Laguerre Vol. 1",,,,Paris,1898,461,468,,1,,

s2hb18,29,,,,,,Heron of Alexandria,,,"Metrica i",,,,,,8,8,,1,,

s2hb19,2,7,10,,,,Herriot J.G.,,,"Methods of Mathematical Analysis and Computation",,,Wiley,New York,1963,,,,1,,

s2hb20,3,16,,,,,Herzberger J.,,,On the R-Order of Convergence of a Class of Simultaneous Methods of Approximating the Roots of a Polynomial in "Numerical Methods and Error bounds" eds. G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,113,119,,1,,

s2hb21,3,7,16,,,,Herzberger J.,Metzner L.,,On the Q-order and R-order of convergence for coupled sequences arising in iterative numerical processes in "Numerical Methods and Error Bounds" Eds. G. Alefeld and J. Herzberger,,,Akademie Verlag,Berlin,1996,120,131,,1,,

s2hb22,13,,,,,,Heymann W.,,,"Studien über die Transformation und Integration der Differential- und Differenzengleichungen",,,Teubner,Leipzig,1891,,,,1,,

s2hb23,17,,,,,,Higham N.J.,,,"Accuracy and Stability of Numerical Algorithms",,,Soc. Ind. Appl. Math.,,1996,,,,1,,

s2hb24,19,25,,,,,Hillman A.P.,Alexanderson G.L.,,"A First Undergraduate Course in Abstract Algebra",,,Wadsworth,Belmont Calif.,1973,,,,1,,

s2hb25,13,,,,,,Hirsch M.,,,"Sammlung von Aufgaben aus der Theorie der Algebraischen Gleichungen",,,,Berlin,1809,,,,1,,

s2hb26,19,20,,,,,Hirschfield J.W.P.,,,"Projective Geometries over Finite Fields",,,Clarendon Press,Oxford,1979,,,,1,,

s2hb27,2,25,,,,,Hollingdale S.,,,"Makers of Mathematics",,,Penguin Books,London,1989,,,,1,,

s2hb28,30,,,,,,Howland J.L.,,,On some methods for computing the roots of polynomials in "Information Processing 1962: Proc. of IFIP Congress 62",,,North-Holland,Amsterdam,1962,116,121,,1,,

s2hb29,20,,,,,,Huang M.D.A.,,,Riemann hypothesis and finding roots over finite fields in "Proc. Seventeenth Ann. ACM Symp. Theor. Comput.",,,Assoc. Comput. Mach.,,1985,121,130,,1,,

s2hb30,25,,,,,,Hungerford T.W.,,,"Algebra",,,Springer-Verlag,New York,1974,,,,1,,

s2hb31,29,,,,,,Hunrath K.,,,"Ueber das Auszichen der Quadratwurzeln bei Greichen und Indern",,,,Hadersleben,1883,,,,1,,

s2hb32,13,,,,,,Hunrath K.,,,"Algebraische Untersuchen nach Tschirnhausens Methode",,,,Glückstadt,1885,,,,1,,

s2hb33,29,,,,,,Hutton C.,,,"A Complete Treatise on Practical Arithmetic and Book-Keeping both by Single and Double Entry",,,G. Ross,Edinburgh,1807,,,,1,,

s2hb34,10,17,19,,,,Hutton C.,,,"A Course of Mathematics",,,,New York,1812,88,88,,1,,

s2hb35,19,29,,,,,Hutton C.,,,"Tracts on Mathematical and Philosophical Subjects Vol. 1",,,Readex Microprint,,1969,210,216,,1,,

s2hb36,29,,,,,,Hwang K.,,,"Computer Arithmetic Principles; Architecture and Design",,,Wiley,,1979,360,366,,1,,

s2hb37,2,10,18,19,25,,Hymers J.,,,"Treatise on the Theory of Algebraical Equations",,,,Cambridge,1858,,,,1,,

s2ij1,27,,,,,,Ibragimov I.A.,Maslova N.B.,,Average number of real roots of random polynomials,Soviet Math. Dokl.,12,,,1971,1004,1008,,1,,

s2ij2,27,,,,,,Ibragimov I.A.,Maslova N.B.,,On the expected number of real zeros of random polynomials. I. Coefficients with zero mean,Theory Probab. Appl.,16,,,1971,228,248,,1,,

s2ij3,27,,,,,,Ibragimov I.A.,Maslova N.B.,,On the expected number of real zeros of random polynomials. II. Coefficients with non-zero means,Theory Probab. Appl.,16,,,1971,485,493,,1,,

s2ij4,27,,,,,,Ibragimov I.A.,Zeitouni O.,,On roots of random polynomials,Trans. Amer. Math. Soc.,349,,,1997,2427,2441,,1,,

s2ij5,15,,,,,,Igarashi H.,Ypma T.,,Relationships between order and efficiency of a class of methods for multiple zeros of polynomials,J. Comput. Appl. Math.,60,,,1995,101,114,,1,,

s2ij6,2,15,,,,,Igarashi H.,Ypma T.,,Empirical versus asymptotic rate of convergence of a class of methods for solving a polynomial equation,J. Comput. Appl. Math.,82,,,1997,229,237,,1,,

s2mj11,3,,,,,,Makrelov E.V.,Semerdzhiev H.I.,Tamburov S.G.,On a generalization of Ehrlich's method (in Russian),C.R. Acad. Bulg. Sci.,39 No. 5,,,1986,43,46,,1,,

s2mj12,3,,,,,,Makrelov I.L.,Semerdziez K.I.,,Methods of finding simultaneously all the roots of algebraic trigonometric and exponential equations,U.S.S.R. Comput. Math. and Math. Phys.,24 No. 5,,,1984,99,105,,1,,

s2mj13,4,,,,,,Malajovich G.,Zubelli J.P.,,A Fast and Stable Algorithm for Splitting Polynomials,Comput. Math. Appl.,33 No. 3,,,1997,1,23,,1,,

s2mj14,30,,,,,,Malek F.,Vaillancourt R.,,On the conditioning of a composite polynomial zerofinding matrix algorithm,C. R. Math. Rep. Acad. Sci. Canada,17,,,1995,67,72,,1,,

s2mj15,30,,,,,,Malek F.,Vaillancourt R.,,Polynomial Zerofinding Iterative Matrix Algorithms,Comput. Math. Appl.,29,,,1995,1,13,,1,,

s2mj16,30,,,,,,Malek F.,Vaillancourt R.,,A Composite Polynomial Zerofinding Matrix Algorithm,Comput. Math. Appl.,30 No. 2,,,1995,37,47,,1,,

s2mj17,2,7,,,,,Maleyx L.,,,Comparison de la méthode d'approximation de Newton à celle dite des parties proportionnelles,Nouv. Ann. Math. Ser. 2,18,,,1879,218,232,,1,,

s2mj18,13,,,,,,Malmsten C.,,,In solutionem Algebraicarum Disquisitio,J. Reine Angew. Math.,34,,,1847,46,74,,1,,

s2mj19,2,,,,,,Malo E.,,,Sur le calcul par approximation des racines des équations numériques. Modification de la formule de Newton.,Nouv. Ann. Math. Ser. 3,11,,,1892,169,178,,1,,

s2mj20,29,,,,,,Mandelbaum D.M.,,,A Method for Calculation of the Square Root Using Combinatorial Logic,J. VLSI Signal Processing,6,,,1993,233,242,,1,,

s2mj21,21,,,,,,Marcellán F.,Pérez T.E.,Pinñar M.A.,Laguerre-Sobolev orthogonal polynomials,J. Comput. Appl. Math.,71,,,1996,245,265,,1,,

s2mj22,13,,,,,,Marik J.,,,On polynomials with all real zeros,Casopis Pest. Mat.,89,,,1964,5,9,,1,,

s2mj23,19,,,,,,Marik J.,,,Real polynomials of the 4th degree,Casopis Pest. Mat.,90,,,1965,33,42,,1,,

s2mj24,29,,,,,,Markstein P.W.,,,Computation of elementary functions on the IBM Risc System/6000 processor,IBM J. Res. Develop.,34,,,1990,111,119,,1,,

s2mj25,19,,,,,,Maschke H.,,,La risoluzione della equazione di sesto grado,Rend. Reale Accad. Lincei Ser. 4,4,,,1888,181,184,,1,,

s2mj26,27,,,,,,Maslova N.,,,On the distribution of the number of real roots of random polynomials,Theory Probab. Appl.,19,,,1974,488,500,,1,,

s2mj27,21,,,,,,Mason E.H. et al,,,Polynomialrecurrencology,Amer. Math. Monthly,103,,,1996,272,273,,1,,

s2mj28,19,,,,,,Matthiessen L.,,,Neue Auflösung der quadratischen cubischen und biquadratischen Gleichungen,Z. Math. Phys.,8,,,1863,133,140,,1,,

s2gj11,10,11,,,,,Gemignani L.,,,Computationally Efficient Applications of the Euclidean Algorithm to Zero Location,Lin. Algebra Appl.,249,,,1996,79,91,,1,,

s2gb3,25,,,,,,Galois E.,,,Analyse d'un Mémoire sur la résolution algébrique des équations in "Oeuvres mathematiques de Galois",,,,,1897,11,12,,1,,

s2gb5,25,,,,,,Galois E.,,,Memoire sur les conditions de résolubilité des equations par radicaux in "Oeuvres Mathématiques",,,Gauthiers-Villars,Paris,1897,33,50,Solution by radicals,1,,

s2gb6,25,,,,,,Galois E.,,,"Ecrits et mémoires mathématiques",,,Gauthier-Villars,Paris,1962,,,,1,,

s2gb7,20,,,,,,Gao S.,von zur Gathen J.,,Berlekamp's and Niederreiter's polynomial factorization algorithms in "Intern. Conf. on Finite Fields" G.L. Mullen et al Eds.,,,Amer. Math. Soc.,,1994,101,116,,1,,

s2gb8,19,25,,,,,Garling D.,,,"Galois Theory",,,Cambridge Univ. Press,,1986,,,,1,,

s2gb9,13,29,,,,,Garnier J.G.,,,"Elemens d'Algèbre",,,,Paris,1811,,,,1,,

s2gb10,20,,,,,,Gauss C.F.,,,Die Lehre von den Resten.II in "Untersuchungen über Höhere Arithmetik von Carl Friedrich Gauss",,,Chelsea,New York,1981,602,629,,1,,

s2gb11,21,,,,,,Gautschi W.,,,Advances in Chebyshev quadrature in "Numerical Analysis Dundee 1975; LNM 506",,,Springer-Verlag,,1976,100,121,,1,,

s2gb12,21,,,,,,Gautschi W.,Milovanovic G.V.,,On a class of complex polynomials having all zeros in a half disk in "Numerical Methods and Approximation Theory" Ed. G.V. Milovanovic,,,,Nis,1984,49,53,,1,,

s2gb13,31,,,,,,Gebhardt A.,,,"Die Auflösung dreigliedriger algebraischer Gleichungen durch Reihen..",,,,Leipzig,1873,,,,1,,

s2gb14,10,,,,,,Geddes K.,Gonnet G.H.,Smedley T.J.,Heuristic Methods for Operations with Algebraic Numbers in "Proc. ISSAC '88: Lecture Notes in Computer Science 358" ed P. Gianni,,,Springer-Verlag,,1988,475,480,,1,,

s2gb15,10,20,,,,,Geddes K.,Labahn G.,Szapor S.,"Algorithms for Computer Algebra",,,Kluwer Academic,,1992,,,Deals with Finite field factorization and GCD's,1,,

,4,5,6,,,,Gerald C.F.,Wheatley P.O.,,Applied Numerical Analysis 6th ed.,,,Addison-Wesley,Reading, Mass.,1999,0,0,Treats Bisection, Newton, Secant, Muller, Bairstow, QD, Graffe, Lehmer, Laguene, and convergence.,1,0,

s2gb17,2,19,,,,,Gerhardt C.I.,,,"Der Briefwechsel von G.W. Leibniz mit Mathematikern",,,Georg Olms,Hildesheim,1962,179,192,,1,,

s2gb18,20,,,,,,Giesbrecht M.,,,Factoring in skew-polynomial rings in "Proc. LATIN '92; Lecture Notes in Computer Science No. 583" Ed. I. Simon,,,Springer-Verlag,,1992,191,203,,1,,

s2gb21,25,,,,,,Goldhaber J.K.,Ehrlich G.,,"Algebra",,,Krieger,,1980,,,,1,,

s2gb22,19,25,,,,,Goldstein L.J.,,,"Abstract Algebra; A First Course",,,Prentice-Hall,Englewood Cliffs N.J,1973,,,,1,,

s2gb23,10,,,,,,Gonzalez-Vega L. et al,,,Sturm-Habicht Sequences in "Proc. ISSAC 1989",,,,,1989,136,146,,1,,

s2gb24,10,,,,,,Gonzalez-Vega L. et al,,,Sturm-Habicht Sequences; Determinants and Real Roots of Univariate Polynomials in "Quantifier Elimination and Cylindrical Algebraic Decompostion" B.F. Caviness and J.R. Johnson Eds.,,,Springer-Verlag,New York,1998,300,316,,1,,

,19,0,0,0,0,0,Eves H.,,,Great Moments in Mathematics (before 1650),,,Math. Ass. Amer.,,1980,0,0,Treats history of solution of cubic and quartic.,1,0,

,20,0,0,0,0,0,Scharlau W.,Opolka H.,,From Fermat to Minkowski: Lectures on the Theory of Numbers and its Historical Development.,,,Springer-Verlag,New York,1985,0,0,Treats quadratic congruences.,1,0,

,20,0,0,0,0,0,Shanks D.,,,Solved and Unsolved Problems in Number Theory.,,,Spartak Books,Washington D.C.,1962,0,0,Treats quadratic congruences.,1,0,

,20,0,0,0,0,0,Burton D.M.,,,Elementary Number Theory. (revised printing),,,Allyn and Bacon,Boston, Mass.,1980,0,0,Treats quadratic congruences.,1,0,

,10,20,0,0,0,0,Schroeder M.R.,,,Number Theory in Science and Communication, (2nd enlarged edn.),,,Springer-Verlag,Berlin, Heidelberg,1986,0,0,Treats GCD's and quadratic congruences.,1,0,

,20,0,0,0,0,0,Devlin K.,,,Microchip Mathematics; Number Theory for Computer Users.,,,Shiva, Chesire,1984,0,0,Treats polynomial congruences.,1,0,

,20,0,0,0,0,0,Grosswald E.,,,Topics from the Theory of Numbers. (2nd edn),,,Birkhauser,Boston,1984,0,0,Treats quadratic congruences.,1,0,

,20,0,0,0,0,0,Shapiro H.N.,,,Indroduction to the Theory of Numbers.,,,Wiley-Interscience,New York,1983,0,0,Treats quadratic congruences.,1,0,

,3,0,0,0,0,0,Ellis G.H.,Watson L.T.,,A parallel algorithm for simple roots of polynomials.,Comput. Math. Appl.,10,,,1984,107,121,Generalized Aberth method, usually faster than Jenkins-Traub or Laguerre. (in parallel mode),1,0,

,29,0,0,0,0,0,Schönhage A.,Grotefeld A.F.W.,Vetter E.,Fast Algorithms: A Multitape Turing Machine Implementation,,,B.I. Wissenschaftsverlag, Mannheim,1994,0,0,Square and Fourth Roots.,1,,

,20,0,0,0,0,0,Borevich Z.I.,Shafarevich I.R.,,Number Theory,,,Academic Press Inc.,,1966,0,0,Considers quadratic congruences and factorization.,1,0,

,17,0,0,0,0,0,Ercegovac M.D.,,,A general hardware-oriented method for evaluation of functions and computations in a digital computer.,IEEE Trans. Comput.,26,,,1987,667,680,Covers parallel evaluation.,1,0,

,1,2,7,14,0,0,Southworth R.W.,Deleeuw S.L.,,Digital computation and numerical methods.,,,McGraw-Hill,New York,1965,0,0,Considers bisection, Newton, Secant, Lin.,1,0,

,20,0,0,0,0,0,Della Dora J.,Di Crescenzo C.,Duval D.,About a new method for computing in algebraic number fields.,Proc. EUROCAL '85,LNCS 204,,,1985,289,290,No note.,1,0,

,10,20,0,0,0,0,Becker, Th.,Weispfenning, V.,,Gröbner Bases, A Computational Approach to Commutative Algebra,Grad. Texts In Mathematics,141,Springer-Verlag,Berlin,1963,0,0,Considers gcd's and factorization over rationals.,1,0,

,20,0,0,0,0,0,Glesser, Ph,Mignotte, M.,,On the smallest divisor of a polynomial,J. Symbolic Computation,17,,,1994,277,282,For a polynomial with integer coefficients, find b such that F has a factor G with |coeff| ≤ b,1,0,

,0,0,0,0,0,0,Jensen, J.L.W.V.,,,Sur un nouvel et important thoreme de la theorie des fonctions,Acta Math.,22,,,1899,359,364,,1,0,

,20,0,0,0,0,0,Kanan, R.,Lenstra, A.K.,Lovász, L.,Polynomial factorization and nonrandomness bits of algebraic and some transcendental numbers.,Math. Comp.,50,,,1988,235,250,,1,0,

,0,0,0,0,0,0,Mignotte, M.,,,An inequality about factors of polynomials,Math. Comp.,28,,,1974,1153,1157,,1,0,

,20,0,0,0,0,0,Mignotte, M.,,,Calcul déterministe des racines d'un polynôme dans un corps fini.,C.R. Acad. Sci. Paris ser. I,306,,,1988,467,472,,1,0,

,18,3,0,0,0,0,Mignotte, M.,Petkovic, M.,Tarjkovic, M.,The root separation of polynomials and some applications,Z. Angew. Math. Mech.,75,,,1995,551,561,Considers localization of roots, convergence of Weierstrass' method, etc.,1,0,

,0,0,0,0,0,0,Nandin,P.,Quitte, C.,,Algorithmique Algebrique,,,Masson,Paris,1992,0,0,,1,0,

,20,0,0,0,0,0,Schinzel, A.,,,On the product of the conjugates outside the unit circle of an algebraic integer,Acta Arith.,24,,,1973,385,399,Bounds products of roots of conjugates of a polynomial,1,0,

,13,0,0,0,0,0,Argyros, I.K.,,,Convergence of general iteration schemes,J. Math. Anal. Appl.,168,,,1992,42,62,,1,0,

,20,0,0,0,0,0,Simmons, G.,,,On the number of irreducible polynomials of degree d over GF(p),Amer. Math. Monthly,77,,,1970,743,745,,1,0,

,2,10,19,25,0,0,Todhunter, I.,,,An Elementary Treatise on the Theory of Equations,,,,Cambridge,1867,0,0,Considers Newton, Sturm, Cubic etc., Existence,1,0,

,19,0,0,0,0,0,Karpinski, L.C.,,,The "Quadripartitum numerorum" of John of Meurs,Bibl. Math. (Ser. 3),13,,,1912,99,114,Medieval treatment of quadratics,1,0,

,29,0,0,0,0,0,Dakhel, A.K.,,,Al-Kashi on Root Extraction,,,American Univ. of Beirut,Beirut,1960,0,0,Extracts n'th roots by method similar to Horner's.,1,0,

,19,0,0,0,0,0,Taton, R.,,,Histoire du Calcul,,,Presses Univer. de France,Paris,1969,0,0,Brief treatment of quadratic in ancient times.,1,0,

,29,0,0,0,0,0,Heilermann,,,Bemerkungen zu den Archimedischen Näherungswerten der irrationalen Quadratwurzeln.,Z. Math. Phys. (hist.-lit. Abt.),26,,,1886,121,126,Square roots among Greeks and Arabs,1,0,

,19,0,0,0,0,0,Cardan(o), G.,,,Opera Omnia,,,Johnson Reprint Corp.,New York,1966,0,0,Original solution of cubic and quadratic,1,0,

,29,0,0,0,0,0,Farmwald, P.M.,,,High Bandwidth Evaluation of Elementary Functions, in "Proc. Fifth IEEE Symp. Comp. Arithmetic",,,,,1981,139,142,Covers square root.,1,0,

,29,0,0,0,0,0,Iordache, C.,Matula, D.W.,,On Infinitely Precise Roundings for Division, Square-Root, Reciprocal and Square-Root Reciprocal, in "Proc. 14th IEEE Symp. Comp. Arithmetic".,,,,,1999,233,240,Covers square root.,1,0,

,29,0,0,0,0,0,Wong, W.F.,Goto, E.,,Fast Hardware-Based Algorithms for Elementary Function Computations Using Rectangular Multipliers,IEEE Trans. Computers,43,,,1994,278,294,Covers square root,1,0,

,29,0,0,0,0,0,Wong, W.F.,Goto, E.,,Fast Evaluation of the Elementary Functions in Single Precision,IEEE Trans. Computers,44,,,1995,453,457,Covers square root,1,0,

,16,0,0,0,0,0,Ko, K.I.,,,Computational Complexity of Roots of Real Functions, in "Proc. 30th IEEE Symp. Foundations of Computer Science",,,,,1989,204,209,GET NOTE,1,0,

,13,0,0,0,0,0,Wylie, A.,,,Chinese Researches,,,,Shanghai,1897,0,0,Brief mention of Horner's method in ancient China,1,0,

,18,21,0,0,0,0,Damianou, P.A.,,,Monic Polynomials in Z[x] with Roots in the Unit Disc,Amer. Math. Monthly,108,,,2001,253,257,There are finitely many monic polynomials of degree n with integer coefficients and all zeros in |z|≤1. All such zeros have modulus 0 or 1.,1,0,

,3,0,0,0,0,0,Petkovic, M.S.,Petkovic, L.D.,,Complex Interval Arithmetic & Its Applications,,,Wiley-VCM,,1998,0,0,Has chapters on "Inclusion of Polynomial Zeros", simultaneous & parallel root-finding.,1,0,

,19,0,0,0,0,0,Lehmann, E.,,,Pocket Calculating the Quartic,Notices Amer. Math. Soc.,41,,,1994,777,779,History and formulas for cubic and quartic.,1,0,

,20,0,0,0,0,0,Andrews, G.,,,Number Theory,,,W.B. Saunders,Philadelphia,1971,0,0,Considers quadratic congruences.,1,0,

,10,0,0,0,0,0,Tanner, H.W.L.,,,A Graphical Representation of the Theorems of Sturm and Fourier,Messenger of Mathematics,18,,,1889,95,99,Title says it.,1,0,

,3,0,0,0,0,0,Tilli, P.,,,Convergence Conditions of Some Methods for the Simultaneous Computation of Polynomial Zeros,Calcolo,35,,,1998,3,15,The convergence of Newton's, Aberth's, and Durand-Kerner's methods for polynomial root finding is analyzed;for each of them convergence theorems and error estimates are provided.,1,0,

,19,0,0,0,0,0,Lohne J.A.,,,A Survey of Herriot's Scientific Writings,Arch. Hist. Exact Sci.,20,,,1979,297,298,Treats some special cubics,1,0,

,19,0,0,0,0,0,Lam L.Y.,,,The Yang Hui Sian Fa: A Thirteenth Century Mathematical Treatise,Chung Chi J.,7,,,1968,171,176,Early Chinese treatment of quadratic.,1,0,

,20,0,0,0,0,0,Hua L.H.,,,Introduction to Number Theory,,,Springer,Berlin,1982,0,0,Treats congruences and factorization of polynomials with rational coefficients,1,0,

,29,0,0,0,0,0,Treutlein,,,Das Rechnen im 16 Jahrhundert,Abh. Gesch. Math,1,,,1877,64,65,Treats square roots,1,0,

s2ij8,21,,,,,,Ismail M.E.H.,Simeonov P.,,Strong asymptotics for Krawtchouk polynomials,J. Comp. Appl. Math.,100,,,1998,121,144,,1,,

s2ij9,29,,,,,,Ito M.,Tagaki N.,Yajima S.,Square rooting by iterative multiply-additions,Inform. Process. Lett.,60,,,1996,267,269,,1,,

s2ij10,29,,,,,,Ito M.,Tagaki N.,Yajima S.,Efficient Initial Approximation for Multiplicative Division and Square Roots by a Multiplication with Operand Modification,IEEE Trans. Comput.,46,,,1997,495,498,,1,,

s2ij11,20,,,,,,Itoh T.,,,An efficient probalistic algorithm for solving quadratic equation over finite fields,Electronics and Communication in Japan,72,,,1989,88,96,,1,,

s2ij12,13,,,,,,Ivanova S.L.,Tarakanovskii L.F.,,Some Properties of Polynomials and Determination of Roots by Parts,Dokl. Math.,56,,,1997,502,504,,1,,

s2ib1,13,,,,,,Ibrahim E.M.,,,Numerical approach to the zeros of polynomials in "IMACS '91" ed. R. Vichnevetsky and J.J.H. Miller,,,,,1991,231,231,,1,,

s2ib4,10,,,,,,Ierardi D.,Kozen D.,,Parallel Resultant Computation in "Synthesis of Parallel Algorithms" J.H. Reif Ed.,,,Morgan Kaufmann,Los Angeles,1993,679,720,,1,,

s2ib5,29,,,,,,Ito M.,Tagaki N.,Yajima S.,Efficient Initial Approximation and Fast Converging Methods for Division and Square Root in "Proc. 12th Symp. Computer Arithmetic",,,,,1995,2,9,,1,,

s2jb1,17,,,,,,Ja Ja J.,,,"An Introduction to Parallel Algorithms",,,Addison-Wesley,Massachusetts,1992,397,402,,1,,

s2jb2,1,2,7,,,,James M.L.,Smith G.M.,Wolford J.C.,"Applied Numerical Methods for Digital Computation",,,Harper Collins,New York,1993,,,,1,,

s2jb4,13,,,,,,Jenks R.D.,Suter R.S.,,"Axiom: The Scientific Computation System Chap. 8",,,Springer-Verlag,New York,1992,,,,1,,

s2jb5,10,19,25,,,,Jerrard G.B.,,,"Mathematical Researches Vol. 2",,,Longman,London,1832,,,,1,,

s2jb6,13,19,25,,,,Jerrard G.B.,,,"An Essay on the Resolution of Equations",,,Taylor and Francis,London,1859,,,,1,,

s2jb7,10,,,,,,Johnson J.R.,,,Algorithms for Polynomial Real Root isolation in "Quantifier Elimination and Cylindrical Algebraic Decomposition" B.F. Caviness and J.R. Johnson Eds.,,,Springer-Verlag,New York,1998,269,299,,1,,

s2jj1,31,,,,,,Jacobi C.G.J.,,,De resolutione aequationum per series infinitas,J. Reine Angew. Math.,6,,,1830,257,286,,1,,

s2jj2,18,,,,,,Jain V.K.,,,On the Location of Zeros of Polynomials,Ann. Univ. Mariae Curie-Sklodowska Sec. A Math.,30 No. 5,,,1976,43,48,,1,,

s2jj3,18,,,,,,Jain V.K.,,,On the zeros of a class of polynomials and related analytic functions,Indian J. Pure Appl. Math.,28,,,1997,533,549,,1,,

s2jj4,29,,,,,,Jamieson M.J.,,,On Rational Function Approximations to Square Roots,Amer. Math. Monthly,106,,,1999,50,52,,1,,

s2jj5,27,,,,,,Jamron B.R.,,,The average number of real zeros of random polynomials,Soviet Math. Dokl.,13,,,1972,1381,1383,,1,,

s2jj6,4,,,,,,Jana P.K.,Sinha B.P.,,Fast Parallel Algorithms for Graeffe's Root Squaring Technique,Comput. Math. Appl.,35 no. 3,,,1998,71,80,,1,,

s2jj7,19,,,,,,Janfroid,,,Question 695,Nouv. Ann. Math. Ser. 2,3,,,1864,399,401,,1,,

s2jj8,2,,,,,,Janni G.,,,Metodo per calcolare con approssimazioni successive certe le radici reali dell'equazioni algebriche,Giorn. Mat.,8,,,1870,157,160,,1,,

s2jj9,25,,,,,,Jerrard G.H.,,,Remarks on M. Hermite's Argument Relating to the Algebraical Resolution of Equations of the Fifth Degree,Phil. Mag.,23,,,1862,146,149,,1,,

s2jj10,25,,,,,,Jerrard G.H.,,,Remarks on M. Hermite's Argument Relating to the Algebraical Resolution of Equations of the Fifth Degree,Phil. Mag.,23,,,1862,469,470,,1,,

s2jj11,19,,,,,,Jerrard G.B.,Hermite C.,,Die Transformation und Auflösung der Gleichungen fünften Grades,Z. Math. Phys.,4,,,1859,77,90,,1,,

s2jj12,10,,,,,,Johnson J.R.,Krandick W.,,Polynomial Real Root Isolation using Approximate Arithmetic,SIGSAM Bull.,31 No. 4,,,1997,56,57,,1,,

s2jj13,25,,,,,,Jordan C.,,,Lettre sur la résolution algébrique des équations,J. Math. Pures Appl. Ser. 2,12,,,1867,105,108,,1,,

s2jj14,25,,,,,,Jordan C.,,,Memoire sur la résolution algébrieque des équations,J. Math. Pures Appl. Ser. 2,12,,,1867,109,157,,1,,

s2jj15,25,,,,,,Jordan C.,,,Théorèmes sur les équations algébriques,J. Math. Pures Appl. Ser. 2,14,,,1869,139,146,,1,,

s2jj16,19,,,,,,Jourdain,,,Méthode pour la résolution des équations litterales du troisième et du quatrième degré,J. Math. Pures et Appl. Ser. 2,4,,,1859,205,208,,1,,

s2jj17,20,,,,,,Jungnickel D.,Vanstone S.A.,,On primitive polynomials over finite fields,J. of Algebra,124,,,1989,337,353,,1,,

s2kj1,27,29,,,,,Kabuo H. et al,,,Accurate rounding scheme for the Newton-Raphson method using redundant binary representation,IEEE Trans. Comput.,43,,,1994,43,50,,1,,

s2kj2,27,,,,,,Kac M.,,,On the average number of real roots of a random algebraic equation,Bull. Amer. Math. Soc.,49,,,1943,314,320,,1,,

s2kj3,27,,,,,,Kac M.,,,On the average number of real roots of a random algebraic equation,Proc. London Math. Soc. Ser. 2,50,,,1948,390,408,,1,,

s2kj5,2,15,,,,,Kalantari B.,Kalantari I.,Zaarenahandi R.,A basic family of iteration functions for polynomial root-finding and its characterizations,J. Comput. Appl. Math.,80,,,1997,209,226,,1,,

s2kj6,21,,,,,,Kaliaguine V.,Ronveaux A.,,On a system of ``classical'' polynomials of simultaneous orthogonality,J. Comput. Appl. Math.,67,,,1996,207,217,,1,,

s2kj7,20,,,,,,Kaltofen E.,Shoup V.,,Subquadratic-time factoring of polynomials over finite fields,Math. Comp,67,,,1998,1179,1197,,1,,

s2kj8,3,,,,,,Kanno S.,Kjurkchiev N.V.,Yamamoto T.,On Some Methods for the Simultaneous Determination of Polynomial Zeros,Japan J. Indust. Appl. Math.,13,,,1996,267,288,,1,,

s2kj9,21,,,,,,Kappert M.,,,On the zeros of the partial sums of cos(z) and sin(z),Numer. Math.,74,,,1996,397,417,,1,,

s2kj10,18,,,,,,Karanicoloff C.,,,On a theorem of type Eneström-Kakeya,Math. Lapok.,14,,,1963,133,136,,1,,

s2kj11,10,,,,,,Karcanias N.,,,Invariance properties and characterization of the greatest common divisor of a set of polynomials,Internat. J. Control,46,,,1987,1751,1760,,1,,

s2kj12,10,,,,,,Karcanias N.,Mitrouli M.,,A matrix pencil based numerical method for the computation of the GCD of polynomials,IEEE Trans. Automat. Control,39,,,1994,977,981,,1,,

s2kj13,28,,,,,,Katsoprinakis E.S.,,,On the Sendov-Ilyeff conjecture,Bull. London Math. Soc.,24,,,1992,449,455,,1,,

s2kj14,20,,,,,,Katz N.M.,,,Factoring polynomials in finite fields: an application of Lang-Weil to a problem in graph theory,Math Ann.,286,,,1990,625,637,,1,,

s2kj15,1,5,,,,,Kavvadias D.J.,Vrakatis M.N.,,Locating and computing all the simple roots and extrema of a function,SIAM J. Sci. Comput.,17,,,1996,1232,1248,,1,,

s2kj16,25,,,,,,Kiernan B.M.,,,The Development of Galois Theory from Lagrange to Artin,Arch. Hist. Exact Science,8,,,1971,40,154,,1,,

s2kj17,19,,,,,,King R.B.,Canfield E.R.,,An Algebraic Algorithm for Calculating the Roots of a General Quintic Equation from its Coefficients,J. Math. Phys.,32,,,1991,823,825,,1,,

s2kj18,2,3,,,,,Kirrinnis P.,,,Partial Fraction Decomposition in C(z) and Simultaneous Newton Iteration for Factorization in C[z],J. Complexity,14,,,1998,378,444,,1,,

s2kj19,18,30,,,,,Kittaneh F.,,,Singular values of companion matrices and bounds on zeros of polynomials,SIAM J. Matrix Anal. Appl.,16,,,1995,333,340,,1,,

s2kj20,21,,,,,,Kjeldgaard A.,,,En Tilnaermelsesvis Beregning af de Reelle Rodder i Ligningen: xⁿ+px+q=0,Tidsskrift fur Mathematik Ser. 4,4,,,1880,135,137,,1,,

s2kj21,3,,,,,,Kjurkchiev N.,,,A Note on the Divergent Starting Points for Euler-Chebyshev's Type Methods,Facta Universitatis (Nis). Ser. Math. Inform.,9,,,1994,95,98,,1,,

s2kj22,3,,,,,,Kjurkchiev N.,,,Initial approximations in Euler-Chebyshev's method,J. Comput. Appl. Math.,58,,,1995,233,236,,1,,

s2kj23,3,,,,,,Kjurkchiev N.,,,A note on the Le Verrier-Fadeev's method,BIT,36,,,1996,182,186,,1,,

s2kj24,3,,,,,,Kjurkchiev N.V.,,,A Note on the Divergent Starting Points for Weierstrass Type Algorithms,Z. Angew. Math. Mech.,76,,,1996,301,302,,1,,

s2kj25,15,,,,,,Kjurkchiev N.,Andreev A.,,Two-sided analog of the Chebyshev's method,C.R. Acad. Bulgare Sci.,41 No. 4,,,1988,17,19,,1,,

s2kj26,3,,,,,,Kjurkchiev N.,Andreev A.,,"title in Russian",Serdica,15,,,1989,302,304,,1,,

s2kj27,3,15,,,,,Kjurkchiev N.,Andreev A.,,on Halley-like algorithms with high order of convergence for simultaneous approximation of multiple roots of polynomials,C.R. Acad. Bulgare Sci.,43 No. 9,,,1990,29,32,,1,,

s2kj28,3,,,,,,Kjurkchiev N.,Ivanov R.,,On Some Multi-Stage Schemes with a Superlinear Rate of Convergence,Ann. Univ. Sofia Fac. Math. et Méc.,78 Livre I,,,1984,132,136,,1,,

s2kj29,3,,,,,,Kjurkchiev N.,Ivanov R.,,On Some Multi-Stage Schemes with a Superlinear Rate of Convergence,Ann. Univ. Sofia Fac. Math. et Méc.,78 Livre I,,,1984,178,185,,1,,

s2kj30,3,,,,,,Kjurkchiev N.,Petkovi\'{c} M.S.,,The Behaviour of Approximations of the SOR Weierstrass Method,Comput. Math. Appl.,32 No. 7,,,1996,117,121,,1,,

s2kj31,3,,,,,,Kjurkchiev N.,Taschev S.,,Method for simultaneous determination of the zeros of a polynomial; in Russian,C.R. Acad. Bulgare Sci.,34,,,1981,1053,1055,,1,,

s2kj32,13,,,,,,Klein F.,,,Ueber eine geometrische Repräsentation der Resolventen algebraischer Gleichungen,Math. Ann.,4,,,1871,346,358,,1,,

s2kj33,19,,,,,,Klein F.,,,Ueber die Auflösung gewisser Gleichungen vom siebenten und achten Grade,Math. Ann.,15,,,1879,251,282,,1,,

s2kj34,19,,,,,,Klein F.,,,Zur theorie der allgemeinen Gleichungen sechsten und siebenten Grades,Math. Ann.,28,,,1887,499,532,,1,,

s2kj35,19,,,,,,Klein F.,,,über die Auflösung der allgemeinen gleichungen fünften und sechsten Grades,Math. Ann.,61,,,1905,50,71,,1,,

s2kj36,20,,,,,,Knopfmacher A.,,,Distinct Degree Factorizations for Polynomials over a Finite Field,SIGSAM Bull.,31 No. 3,,,1997,38,39,,1,,

s2kj37,20,,,,,,Knopfmacher A.,Knopfmacher J.,,Counting polynomials with a given number of zeros in a finite field,Linear and Multilinear Algebra,26,,,1990,287,292,,1,,

s2kj38,20,,,,,,Knopfmacher A.,Knopfmacher J.,,Counting irreducible factors of polynomials over a finite field,Discrete Math.,112,,,1993,103,118,,1,,

s2kj39,20,,,,,,Knopfmacher A.,Warlimont R.,,Distinct degree factorizations for polynomials over a finite field,Trans. Amer. Math. Soc.,347,,,1995,2235,2243,,1,,

s2kj40,19,,,,,,Kobayashi S.,Nakagawa H.,,Resolution of Solvable Quintic Equations,Math. Japonica,37,,,1992,883,883,,1,,

s2kj41,2,,,,,,Kollerstrom N.,,,Thomas Simpson and ``Newton's method of approximation'': an enduring myth,British J. Hist. Sci.,25,,,1992,347,354,,1,,

s2kj42,25,,,,,,König,,,Ueber rationale Functionen von n Elementen und die allgemeine Theorie der algebraischen Gleichungen,Math. Ann.,14,,,1879,212,230,,1,,

s2kj43,29,,,,,,Kostopoulos G.K.,,,Computing the square root of binary numbers,Computer Design,11 No. 8,,,1972,53,57,,1,,

s2kj44,18,,,,,,Kova\v{c}evi\'{c} M.A.,Milovanovi\'{c} I.Z.,,On a generalization of the Eneström-Kakeya Theorem,Pure Math. Appl. Ser. A,3,,,1992,43,47,,1,,

s2kj45,13,,,,,,Kozen D.,Landau S.,,Polynomial decomposition algorithms,J. Symb. Comput.,7,,,1989,445,456,,1,,

s2kj46,28,,,,,,Kramer H.,,,über einige ungleichungen zwischen den nullstellen eines polynoms und seinen ersten ableitung,Mathematica (Cluj),10 (33) No. 1,,,1968,89,93,,1,,

s2kj47,13,,,,,,Krandick W.,,,Komplexe Nullstellen von Polynomen-Vergleich zweier unfehlbarer Methoden,Z. Angew. Math. Mech.,75 Supp,,,1995,537,538,,1,,

s2kj48,18,,,,,,Kraus L.,,,Limites des racines d'une équation n'ayant que des racines réelles,Nouv. Ann. Math. Ser. 3,18,,,1899,301,305,,1,,

s2kj49,19,,,,,,Kronecker L.,,,Gleichungen der siebenten Grades,Mon. Kgl. Preuss. Akad. Wiss. Ber.,,,,1858,287,289,,1,,

s2kj50,19,,,,,,Kronecker L.,,,über die algebraischen Gleichungen; von denem die Thielung der elliptischen Functionen abhängt,Mon. Kgl. Preuss. Akad. Wiss. Ber.,,,,1875,498,507,,1,,

s2kj51,25,,,,,,Kronecker L.,,,Abhandlung über Abelsche Gleichungen,Mon. Kgl. Preuss. Akad. Wiss. Ber.,,,,1877,845,851,,1,,

s2kj52,19,25,,,,,Kronecker L.,,,Entwickelungen aus der Theorie der algebraischen Gleichungen,Mon. Kgl. Preuss. Akad. Wiss. Ber.,,,,1879,205,229,,1,,

s2kj53,21,,,,,,Kroó A.,Peherstorfer F.,,On the zeros of minimal L_p-norm,Proc. Amer. Math. Soc.,101,,,1987,652,656,,1,,

s2kj54,21,,,,,,Kuijlaars A.B.J.,,,The zeros of Faber polynomials generated by an m-star,Math. Comp.,65,,,1996,151,156,,1,,

s2kj55,20,21,,,,,Kuijlaars A.B.J.,Raklimanoe E.A.,,Zero distributions for discrete orthogonal polynomials,J. Comp. Appl. Math.,99,,,1998,255,274,,1,,

s2kj56,21,,,,,,Kumaresan R.,,,On the zeros of the linear prediction-error filters for deterministic signals,IEEE Trans. Acoust. Speech Signal Process.,29,,,1983,217,221,,1,,

s2kj57,18,,,,,,Kunieda M.,,,Note on the roots of algebraic equations,Tohoku Math. J.,9,,,1916,167,73,,1,,

s2kb1,1,2,7,,,,Kahaner D.,Moler C.,Nash S.,"Numerical Methods and Software",,,Prentice-Hall,Englewood Cliffs NJ,1989,235,271,,1,,

s2kb2,10,20,,,,,Kaltofen E.,,,Polynomial factorization 1987-1991 in "Proceedings of Latin '92; LNCS 583" I. Simon ed.,,,Springer-Verlag,,1992,294,313,,1,,

s2mj29,19,,,,,,Matthiessen L.,,,Ueber ein Beziehung der Seiten und Diagonalen eines Kreisvierichs zu den Wurzeln einer biquadratischen Gleichung und ihrer Resolvente,Z. Math. Phys.,10,,,1865,331,332,,1,,

s2mj30,7,19,,,,,Matthiessen L.,,,Die Regel vom falschen Satze bei den Indern und Arabern des Mittel-alters und eine bemerkenswerthe Anwendung desselben zur directen Auflösung der quadratischen und cubischen Gleichungen,Z. Math. Phys.,15,,,1870,41,47,,1,,

s2mj31,19,20,,,,,Matveeva M.V.,,,Solutions of Equations of the Third Degree in a Field of Characteristic 3,Problems of Information Transmission,4 No. 4,,,1968,64,66,,1,,

s2mj32,19,25,,,,,McClintock E.,,,On the Resolution of Equations of the Fifth Degree,Amer. J. Math.,6,,,1884,301,315,,1,,

s2mj33,19,25,,,,,McClintock E.,,,Analysis of Quintic Equations,Amer. J. Math.,8,,,1886,45,84,,1,,

s2mj34,13,,,,,,McNamee J.M.,,,A Supplementary Bibliography on Roots of Polynomials,J. Comput. Appl. Math.,78,,,1997,1,1,,1,,

s2mj35,2,24,,,,,McNamee J.M.,,,A Comparison of Methods for Accelerating Convergence of Newton's Method for Multiple Polynomial Roots,SIGNUM,33 No 2,,,1998,17,22,,1,,

s2mj36,29,,,,,,McQuillan S.E.,McCanny J.V.,,VLSI module for high-performance multiply square root and divide,IEE Proc. E: Computers and Digital Techniques,139,,,1992,505,510,,1,,

s2mj37,29,,,,,,McQuillan S.E.,McCanny J.V.,Woods R.F.,High performance VLSI architecture for division and square root,Electron. Lett.,27 No. 1,,,1991,19,21,,1,,

s2mj38,28,,,,,,Meier A.,Sharma A.,,On Ilyeff's conjecture,Pacific J. Math.,31,,,1969,459,467,,1,,

s2mj39,21,,,,,,Meijer H.G.,,,Coherent pairs and zeros of Sobolev-type orthogonal polynomials,Indag. Math. (N.S.),4,,,1993,163,176,,1,,

s2mj40,21,,,,,,Meijer H.G.,,,Sobolev orthogonal polynomials with a small number of real zeros,J. Approx. Theory,77,,,1994,305,313,,1,,

s2mj41,13,,,,,,Mellin H.,,,Zur Theorie der trinomischen Gleichungen,Ann. Acad. Sci. Fenn. Ser. A,7 No. 7,,,1915,3,32,,1,,

s2mj42,19,,,,,,Mellin H.,,,Résolution de l'équation algébrique générale à l'aide de la fonction Γ,C.R. Acad. Sci. Paris,172,,,1921,658,661,,1,,

s2mj43,2,7,2,,,,Melman A.,,,Numerical solution of a secular equation,Num. Math.,69,,,1995,483,493,,1,,

s2mj44,15,,,,,,Melman A.,,,Geometry and Convergence of Euler's and Halley's Method,SIAM Rev.,39,,,1997,728,735,,1,,

s2mj45,13,,,,,,Mehmke R.,,,Neue Methode; beliebige numerische Gleichungen mit einer Unbekannten graphisch aufzulösen,Der Civilingenieur,35,,,1889,617,634,,1,,

s2mj46,25,31,,,,,Méray C.,,,Méthode directe fondée sur l'emploi des séries pour prouver l'existence des racines des équations entières a une inconnue par la simple exécution de leur calcul numérique,Bull. Sci. Math. Ser. 2,15,,,1891,236,252,,1,,

s2mj47,19,,,,,,Meyer W.W. et al,,,Complex Roots of Special Quartic Polynomials,Amer. Math. Monthly,102,,,1995,277,277,,1,,

s2lj1,20,21,,,,,Lagarias J.C.,,,Modular Fekete Polynomials,Amer. Math. Monthly,105,,,1998,370,371,,1,,

s2lj2,31,,,,,,Lagrange,,,Nouvelle méthode pour résoudre les équations littérales par le moyen des séries,Oeuvres,3,,,1867,5,73,see also Readex Microprint 1970,1,,

s2lj3,18,,,,,,Lagrange,,,Recherche sur la determination du nombre des racines imaginaires dans les équations literales,Oeuvres,4,,,1867,343,374,see also Readex Microprint 1970,1,,

s2lj4,10,,,,,,Laguerre E.,,,Sur la règle des signes de Descartes,Nouv. Ann. Math. Ser. 2,18,,,1879,5,13,,1,,

s2lj5,18,21,,,,,Laguerre E.,,,Sur une propriété des polynômes X_n de Legendre,C.R. Acad. Sci. Paris,41,,,1880,849,851,,1,,

s2lj6,15,,,,,,Laguerre E.,,,Sur une méthode pour obtenir par approximation les racines d'une équation algébriques qui a toutes ses racine réelles,Nouv. Ann. Math. Ser. 2,19,,,1880,161,171,,1,,

s2lj7,2,,,,,,Laguerre E.,,,Sur l'approximation des racine des équations algébriques,Nouv. Ann. Math. Ser. 3,3,,,1884,113,120,,1,,

s2lj8,13,,,,,,Lahaye E.,,,Une méthode de résolution des équations algébriques,C.R. Acad. Sci. Paris,196,,,1933,742,744,,1,,

s2lj9,13,,,,,,Lahaye E.,,,Sur la représentation des racines des équations algébriques,Acad. Roy. Sci. Lett. et B-Arts Belg. Bull. Cl. Sc,27,,,1941,418,427,,1,,

s2lj10,5,31,,,,,Laisant A.,,,Sur les séries récurrentes; dans leur rapports avec les équations,Bull. Sci. Math. Astr. Ser. 2,5,,,1881,218,249,,1,,

s2lj11,31,,,,,,Lambert J.H.,,,Observationes Variae in Mathesin Puram,Acta Helvetica,3,,,1758,128,168,,1,,

s2lj12,31,,,,,,Lambert P.A.,,,New applications of Maclaurin's series in the solution of equations and in the expansion of functions,Proc. Amer. Phil. Soc.,42,,,1903,85,95,,1,,

s2lj13,31,,,,,,Lambert P.A.,,,Solution of algebraic equations in infinite series,Proc. Amer. Phil. Soc.,47,,,1908,111,115,,1,,

s2lj14,31,,,,,,Lambert P.A.,,,On the solution of algebraic equations in infinite series,Bull. Amer. Math. Soc. Ser. 2,14,,,1908,467,477,,1,,

s2lj15,20,,,,,,Landau S.,,,Factoring polynomials over algebraic number fields (Erratum),SIAM J. Comput.,20,,,1991,998,998,,1,,

s2lj16,29,,,,,,Lang T.,Montuschi P.,,Higher radix square root with prescaling,IEEE Trans. Comput.,41,,,1992,996,1009,,1,,

s2lj17,20,,,,,,Lange E.,,,Substitutions for Linear Shift Register Sequences and the Factorization Algorithms of Berlekamp and Niederreiter,Lin. Algebra Appl.,249,,,1996,217,228,,1,,

s2lj18,20,,,,,,Lasker,,,über eine Eigenschaft der Diskriminante,Arch. Math. Phys.,25,,,1916,176,178,,1,,

s2lj19,19,,,,,,Lebesgue V.A.,,,Sur la résolution des équations du quatrième degré,Nouv. Ann. Math.,17,,,1858,386,390,,1,,

s2mj48,21,,,,,,Mhaskar H.N.,Saff E.B.,,On the distribution of zeros of polynomials orthogonal on the unit circle,J. Approx. Theory,63,,,1990,30,38,,1,,

s2mj49,21,,,,,,Mhaskar H.N.,Saff E.B.,,The distribution of zeros of asymptotically extremal polynomials,J. Approx. Theory,65,,,1991,279,300,,1,,

s2mj50,2,,,,,,Michel Ch.,,,Sur les methodes d'approximation,Rev. Math. Spec.,8,,,1905,89,90,see also pp 113-116,1,,

s2mj51,20,,,,,,Mignotte M.,,,Un algorithme sur la décomposition des polynomes dans un corps fini.,C.R. Acad. Sci. Paris,280A,,,1969,137,139,,1,,

s2mj52,20,,,,,,Mignotte M.,,,Factorization of univariate polynomials: a statistical study,ACM SIGSAM,14 No. 4,,,1980,41,44,,1,,

s2mj53,18,,,,,,Mignotte M.,,,On the Product of the Largest Roots of a Polynomial,J. Symb. Comput.,13,,,1992,605,611,,1,,

s2mj54,20,,,,,,Mignotte M.,Nicolas J.L.,,Statistiques sur F_q[X],Ann. Inst. Henri Poincaré,19,,,1983,113,121,,1,,

s2mj55,20,29,,,,,Mignotte M.,Schnorr C.,,Calcul des racines d-ièmes dans un corps fini,C. R. Acad. Sci. Paris,290A,,,1980,205,206,,1,,

s2mj56,29,,,,,,Mikami N.,Kobayashi M.,Yokoyama Y.,A new DSP-Oriented algorithm for calculation of the Square-Root using a nonlinear digital filter,IEEE Trans. Signal Processing,40,,,1992,1663,1669,,1,,

s2mj57,19,,,,,,Mikami Y.,,,A Remark on the Chinese Mathematics in Cantor's Geschichte der Mathematik,Arch. Math. Phys. Ser. 3,15,,,1909,68,70,,1,,

s2mj58,23,,,,,,Mikhailov N.N.,,,Electric devices for solving algebraic equations,Autom. Remote Control,19 No. 5,,,1958,472,486,,1,,

s2mj59,28,,,,,,Miller M.,,,Maximal polynomials and the Ilieff-Sendov conjecture,Trans. Amer. Math. Soc.,321,,,1990,285,303,,1,,

s2mj60,28,,,,,,Miller M.J.,,,Continuous independence and the Ilieff-Sendov conjecture,Proc. Amer. Math. Soc.,115,,,1992,79,83,,1,,

s2mj61,17,26,,,,,Miller W.,,,Computational complexity and numerical stability,SIAM J. Comput.,4,,,1975,97,107,,1,,

s2mj62,10,18,,,,,Milner I.,,,Observations on the Limits of Algebraical Equations...,Philos. Trans. Roy. Soc. London,68,,,1778,382,386,,1,,

s2mj63,19,20,,,,,Mirimanoff,,,Sur les congruences des troisième degré,L'Enseignement Math.,9,,,1907,381,384,,1,,

s2mj64,10,,,,,,Mitrouli M.,Karcanias N.,,Computation of the GCD of polynomials using Gaussian transformation and shifting,Internat. J. Control,58,,,1993,211,228,,1,,

s2mj65,10,,,,,,Mitrouli M.,Karcanias N.,Koukouvinos C.,Numerical performance of the matrix-pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies,J. Comput. Appl. Math.,76,,,1996,89,112,,1,,

s2kb3,3,,,,,,Kanno S.,Yamamoto T.,,Validated computation of polynomial zeros by the Durand-Kerner method II in "Topics in Validated Computation" Ed. J. Herzberger,,,North Holland,Amsterdam,1994,55,61,,1,,

s2kb4,10,,,,,,Karcanias N.,,,System theoretic characterizations of the greatest common divisor of a set of polynomials in "Applications of Matrix Theory" eds. M.J.C. Gover and S. Barnett,,,Clarendon Press,,1989,237,248,,1,,

s2kb5,21,,,,,,Karlin S.,Pinkus A.,,Gaussian quadrature formulae with multiple nodes in "Studies in Spline Functions and Approximation Theory",,,Academic Press,New York,1976,113,162,,1,,

s2kb6,10,,,,,,Katter F.,,,"Ueber die Resultante zweier Gleichungen n^ten Grades",,,Putbus,,1876,3,22,,1,,

s2kb7,19,,,,,,Kawai,Kyutoku,,"Kaishiki Shimpo: New method of solving equations",,,,,1803,,,,1,,

s2kb8,19,,,,,,Kazuyuki S.,,,"Kokon Sampo-ki: Old and New Methods of Mathematics",,,,,1670,,,,1,,

s2kb9,19,,,,,,King R.B.,,,"Beyond the Quartic Equation",,,Birkhauser,,1996,,,,1,,

s2kb11,3,,,,,,Kjurkchiev N.V.,,,"Initial Approximations and Root Finding Methods",,,Wiley-VCH,Weinheim Germany,1998,,,,1,,

s2kb12,19,25,,,,,Klein F.,,,"Lectures on Mathematics; Evanston Colloquium",,,Macmillan,New York,1894,67,74,,1,,

s2kb13,20,,,,,,Knopfmacher A.,Knopfmacher J.,Warlimont R.,Lengths of factorization for polynomials over a finite field in "Finite Fields: Theory; Applications; and Algorithms; Contemporary Mathematics Vol. 168" Eds. G.L. Mullen and P.J.S. Shiue,,,Amer. Math. Soc.,,1994,185,205,,1,,

s2kb14,1,2,7,15,,,Köckler N.,,,"Numerical Methods and Scientific Computing",,,,Oxford,1994,123,148,,1,,

s2kb15,29,,,,,,Koren I.,,,"Computer Arithmetic Algorithms",,,Prentice Hall,Englewood Cliffs,1993,,,,1,,

s2kb16,17,,,,,,Kosaraju S.R.,,,Parallel Evaluation of Division-Free Arithmetic Expressions in "Proc. Symposium on Theory of Computing",,,,,1986,231,239,,1,,

s2kb17,27,,,,,,Kostlan E.,,,On the distribution of roots of random polynomials in "From Topology to Computation: Proceedings of the Smallfest" M.W. Hirsch et al eds.,,,Springer-Verlag,New York,1993,419,431,,1,,

s2kb18,1,2,7,,,,Kowalski M.A.,Sikorski K.A.,Stenger F.,"Selected Topics in Approximation and Computation",,,Oxford University Press,,1995,334,341,,1,,

s2kb19,19,25,,,,,Kramer E.,,,"The Nature and Growth of Modern Mathematics",,,Hawthorn,New York,1970,,,,1,,

s2kb20,12,15,,,,,Kreier N.,Shellucci P.,,Einschliessungen von Polynom-Nullstellen in "Interval Mathematics" K. Nickel Ed.,,,,,1975,223,228,,1,,

s2kb21,21,,,,,,Krylov V.I.,,,"Approximate Calculation of Integrals" Trans. A.H. Stroud,,,MacMillan,London,1962,,,,1,,

s2kb22,6,,,,,,Kupka I.,,,Die numerische Bestimmung mehrfacher und nahe benachbarter Polynom-nullstellen nach einem Bernoulli-Verfahren in "Constructive Aspects of the Fundamental Theorem of Algebra",,,Wiley,New York,1974,181,191,,1,,

s2kb23,29,,,,,,Kwan H.,Nelson R.L. Jr.,Swartzlander E.E. Jr.,Cascaded Implementation of an Iterative Inverse Square-Root Algorithm with Overflow Lookahead in "Proc. 12th Symp. Computer Arithmetic",,,,,1995,124,131,,1,,

s2lj20,2,15,,,,,Lee I.,Jung G.,,A generalized Newton-Raphson method using curvature,Communications in Numerical Methods in Engineering,11,,,1995,757,763,,1,,

s2lj21,29,,,,,,Lenaerts E.H.,,,Automatic square rooting,Electron. Engng.,27,,,1955,287,289,,1,,

s2lj22,21,,,,,,Lenstra H.W.,Schoof R.J.,,Primitive normal bases for finite fields,Math. Comp.,48,,,1987,217,232,,1,,

s2lj23,20,,,,,,Leonard P.A.,Williams K.S.,,Quartics over GF(2ⁿ),Proc. Amer. Math. Soc.,36,,,1972,347,350,,1,,

s2lj24,17,,,,,,Leoncini M.,,,On Speed versus Accuracy: Some Case Studies,J. Complexity,12,,,1996,239,253,,1,,

s2lj25,22,,,,,,Leopold E.,,,The extremal zeros of a perturbed orthogonal polynomials system,J. Comp. Appl. Math.,98,,,1998,99,120,,1,,

s2lj26,18,21,,,,,Leopold E.,,,Location of the zeros of orthogonal polynomials with an automataic procedure I,J. Comput. Appl. Math,92,,,1998,1,14,,1,,

s2lj27,21,,,,,,Lether F.G.,Wenston P.R.,,Minimax approximations to the zeros of P_n(x) and Gauss-Legendre quadrature,J. Comput. Appl. Math.,59,,,1995,245,252,,1,,

s2lj28,17,,,,,,Li L.,Hu J.,Nakamura T.,A simple parallel algorithm for polynomial evaluation,SIAM J. Sci. Comput.,17,,,1996,260,262,,1,,

s2lj29,20,,,,,,Lidl R.,Matthews R.W.,,Galois: an Algebra Microcomputer Package,Congressus Numerantium; Winnipeg,66,,,1988,145,155,,1,,

s2lj30,29,,,,,,Liggett T.M.,Petersen P.,,The Law of Large Numbers and $\sqrt{2}$ ,Amer. Math. Monthly,102,,,1995,31,35,,1,,

s2lj31,29,,,,,,Lim P.K.,Sidahmed M.A.,Jullien G.A.,High speed architectures for approximate fixed-point division and square-root,International J. of Electronics,67,,,1989,329,342,,1,,

s2lj32,2,12,,,,,Lin Q.,Rokne J.G.,,An interval iteration for multiple roots of transcendental equations,BIT,35,,,1995,561,571,,1,,

s2lj33,17,,,,,,Lin Q.,Rokne J.,,Methods for bounding the range of a polynomial,J. Comput. Appl. Math.,58,,,1995,193,199,,1,,

s2lj34,11,,,,,,Lin Q.,Rokne J.,,A circular splitting search algorithm for systems of complex equations,J. Comput. Appl. Math.,75,,,1996,119,129,,1,,

s2lj35,13,,,,,,Lindemann F.,,,über die Auflösung algebraischer Gleichungen durch transcendente Functionen I,Göttingen Nach.,,,,1894,245,249,,1,,

s2lj36,13,,,,,,Lindemann F.,,,über die Auflösung algebraischer Gleichungen durch transcendente Functionen II,Göttingen Nach.,,,,1892,292,298,,1,,

s2lj37,18,30,,,,,Linden H.,,,Bounds for the Zeros of Polynomials from Eigenvalues and Singular Values of Some Companion Matrices,Lin. Algebra Appl.,271,,,1998,41,82,,1,,

s2lj38,20,29,,,,,Lindgren M.,,,Polynomial solutions of binomial congruences,J. Austral. Math. Soc.,1,,,1960,257,280,,1,,

s2lj39,20,,,,,,Liu Z.,Wang P.S.,,Height as a Coefficient Bound for Univariate Polynomial Factors,SIGSAM Bull.,28 No. 2,,,1994,20,27,,1,,

s2lj40,20,,,,,,Liu Z.,Wang P.S.,,Height as a Coefficient Bound for Univariate Polynomial Factors II,SIGSAM Bull.,28 No. 3/4,,,1994,1,9,,1,,

s2lj41,20,,,,,,Lloyd D.B.,Remmers H.,,Polynomial factor tables over finite fields,Mathematical Algorithms,2,,,1967,85,99,,1,,

s2lj42,19,,,,,,Lobatto R.,,,Sur une propriété relative aux racines d'une classe particulière d'équations du troisième degré,J. Math. Pures Appl.,9,,,1844,177,192,,1,,

s2lj43,2,,,,,,Lobatto R.,,,Sur quelques nouveaux caractères propre à reconnaître l'imaginarité de deux racines d'une équation numérique situées entre des limites données,J. Math. Pures Appl.,9,,,1844,295,309,,1,,

s2lj44,3,,,,,,LoCascio M.L.,Pasquini L.,Trigiante D.,Simultaneous Determination of Polynomial Roots and Multiplicities: an Algorithm and Related Problems,Ricerche di Matematica,38,,,1989,283,305,,1,,

s2lj45,2,10,14,,,,Locher F.,Skrzipek M.R.,,An Algorithm for Locating all Zeros of a Real Polynomial,Computing,54,,,1995,359,375,,1,,

s2lj46,19,,,,,,Lockhart J.,,,Letter to Mr. Cockle,Mechanics Magazine,53,,,1850,449,449,,1,,

s2lj47,19,,,,,,Lockhart J.,,,Letter to Mr. Cockle,Mechanics Magazine,55,,,1851,173,173,,1,,

s2lj48,2,,,,,,Lohnstein T.,,,Eine Methode zur numerischen Auflösung einer algebraischen Gleichungen,Z. Math. Phys.,36,,,1891,383,384,,1,,

s2lj49,20,,,,,,Long A.F.,,,Factorization of irreducible polynomials over a finite field with the substitution x^{q^r}-x for x,Acta Arith.,25,,,1973,65,80,,1,,

s2lj50,20,,,,,,Long A.F.,Vaughan T.P.,,Factorization of Q (h(t))(x) over a Finite Field where Q(x) is Irreducible and h(T)(x) is Linear. I,Linear Algebra Appl.,13,,,1976,207,221,,1,,

s2lj51,20,,,,,,Long A.F.,Vaughan T.P.,,Factorization of Q (h(t))(x) over a Finite Field where Q(x) is Irreducible and h(T)(x) is Linear. II,Linear Algebra Appl.,11,,,1975,53,72,,1,,

s2lj52,25,,,,,,Loria G.,,,Esame di alcune ricerche concernenti l'esistenza di radici nelle equazioni algebriche,Bibl. Math. Ser. 2,5,,,1891,99,112,see also ibid Vol. 7 (1893) 47-50,1,,

s2lj53,19,,,,,,Loria G.,McLenon R.B.,,The Debt of Mathematics to the Chinese People,Scientific Monthly,12,,,1921,517,521,,1,,

s2lj54,18,,,,,,Lossers O.,,,Untitled,Amer. Math. Monthly,78,,,1971,681,683,,1,,

s2lj55,20,,,,,,Lubelski S.,,,Zur Reduzibilitat von Polynomen in der Kongruenztheorie,Acta Arith.,1,,,1936,169,183,,1,,

s2lj56,21,,,,,,Lubinsky D.S.,,,The Weighted L_p Norms of Orthonormal Polynomials for Erdös Weights,Comput. Math. Appl.,33 No. 1/2,,,1997,151,163,,1,,

s2lj57,2,29,,,,,Luckey P.,,,Die Ausziehung der n-ten Wurzel und der binomische Lehrzatz in der islamischen Mathematik,Math. Ann.,120,,,1948,217,274,,1,,

s2lj58,3,14,,,,,Luk W.S.,,,Finding roots of a real polynomial simultaneously by means of Bairstow's method,BIT,36,,,1996,302,308,,1,,

s2lj59,23,,,,,,Lukaszewicz L.,,,A Simplified Solution and New Application of an Analyser of Algebraic Polynomials,Bull. Polish Acad. Sci. Cl IV,1,,,1953,103,107,,1,,

s2lj60,19,,,,,,Luther E.,,,Ueber die Factoren der algebraische lösbaren irreducibeln Gleichungen vom sechsten Grade und ihren Resolventen,J. Reine Angew. Math.,37,,,1848,193,220,,1,,

s2lb1,19,,,,,,Lacroix S.F.,,,"Complement des élémens d'Algèbre",,,Courcier,Paris,1817,,,,1,,

s2lb2,17,,,,,,Lakshmivarahan S.,Dhall S.K.,,"Analysis and Design of Parallel Algorithms",,,McGraw-Hill,New York,1990,254,283,,1,,

s2lb3,29,,,,,,Lang T.,Montuschi P.,,Very-high radix combined division and square root with prescaling and selection by rounding in "Proc. 12th IEEE Symposium on Computer Arithmetic",,,IEEE,,1995,124,131,,1,,

s2lb4,10,,,,,,Langemyr L.,,,An asymptotically fast probabilistic algorithm for computing polynomial gcd's over an algebraic number field in "Applied Algebra Algebraic Algorithms and Error-Correcting Codes" S. Sakata Ed.,,,Springer-Verlag,,1990,222,233,,1,,

s2lb5,10,,,,,,Langemyr L.,McCallum. S.,,The Computation of Polynomial Greatest Common Divisors Over an Algebraic Number Field in "Proc. EUROCAL '87; LNCS 378",,,Springer-Verlag,,1987,298,299,,1,,

s2lb6,19,,,,,,Langley E.M.,,,"A Treatise on Computation",,,Longman,,1910,,,,1,,

s2lb7,2,10,19,25,,,Laurent H.,,,"Traité d'Algèbre",,,,,1887,,,,1,,

s2lb8,20,,,,,,Lehmer D.H.,,,Computer technology applied to the theory of numbers in "Studies in Number Theory" ed. W.J. Leveque,,,Math. Assoc. Amer.,,1969,117,151,,1,,

s2lb9,20,,,,,,Lenstra A.K.,,,Factorization of Polynomials in "Computational Methods in Number Theory; Part I" H.W. Lenstra and R. Tijdeman eds.,,,Math. Centrum,,1982,169,198,,1,,

s2lb10,1,2,7,,,,Lerman S.R.,,,"Problem Solving and Computation for Scientists and Engineers: An Introduction using C",,,Prentice-Hall,,1973,,,,1,,

s2lb11,19,,,,,,Ley,,,"Ueber einige besondere Auflösungen der Gleichungen des vierten Grades",,,,Koln,1849,,,,1,,

s2lb12,19,,,,,,Li Juan,,,"Theory of Equations K'ai-fang Shuo",,,,,1800,,,,1,,

s2lb13,13,,,,,,Libri G.,,,"Histoire des Sciences Mathematiques en Italie",,,Georg Olms,Hildesheim,1967,,,,1,,

s2lb15,20,,,,,,Lidl R.,Niederreiter H.,,"Finite Fields 2/E",,,Cambridge Univ. Press,,1997,,,,1,,

s2lb16,20,,,,,,Lidl R.,Pilz G.,,"Applied Abstract Algebra",,,Springer- Verlag,New York,1984,,,,1,,

s2lb17,25,,,,,,Lieber L.R.,,,"Galois and the Theory of Groups",,,Galois Institute,,1956,,,,1,,

s2lb18,2,10,19,,,,Lobatto R.,,,"Recherches sur la distinction des racines réelles et imaginaires dans les équations numérique...",,,Bachelier,Paris,1842,,,,1,,

s2lb19,19,,,,,,Lockhart J.,,,"A Method of Approximating Towards the Roots of Cubic Equations...",,,,London,1813,,,,1,,

s2mj66,10,,,,,,Mitrouli M.,Karcanias N.,Koukouvinos C.,Further numerical aspects of the ERES algorithm for the computation of the greatest common divisor of polynomials and comparison with other existing methodologies,Utilitas Mathematica,50,,,1996,65,84,,1,,

s2mj67,2,10,5,,,,Mittal R.C.,Agarwal R.,,On zeros of a complex polynomial,Indian J. Pure Appl. Math.,26,,,1995,363,371,,1,,

s2mj68,3,,,,,,Miyakoda T.,,,Iterative methods for multiple zeros of a polynomial by clustering,J. Comput. Appl. Math.,28,,,1989,315,326,,1,,

s2mj69,3,,,,,,Miyakoda T.,,,Balanced convergence of iterative methods to a multiple zero of a complex polynomial,J. Comput. Appl. Math.,39,,,1992,201,212,,1,,

s2mj70,20,,,,,,Moak D.,Saff E.,Varga R.,On the zeros of Jacobi polynomials P_n^(α_n,β_n),Trans. Amer. Math. Soc.,249,,,1979,159,162,,1,,

s2mj71,18,,,,,,Mohammad Q.,,,On the zeros of polynomials,Amer. Math. Monthly,72,,,1965,35,38,,1,,

s2mj72,2,,,,,,Moigno,,,Exposition de la méthode de Cauchy,Nouv. Ann. Math.,10,,,1851,14,22,,1,,

s2mj73,26,,,,,,Moiser R.G.,,,Root neighbourhoods of a polynomial,Math. Comp.,47,,,1986,265,273,,1,,

s2mj74,20,,,,,,Monagan M.B.,,,A heuristic irreducibility test for univariate polynomials,J. Symb. Comput.,13 No. 1,,,1992,47,57,,1,,

s2mj75,20,,,,,,Monagan M.B.,,,von zur Gathen's Factorization Challenge,SIGSAM Bull.,27 No. 2,,,1993,13,18,,1,,

s2ab1,20,,,,,,Abbot J.A.,Davenport J.H.,,Polynomial factorization: an exploration of Lenstra's algorithm in "EUROCAL '87 LNCS 378" J.H. Davenport ed.,,,Springer-Verlag,New York,1987,391,402,,1,,

s2ab2,1,2,3,,,,Aberth O.,,,"Precision Numerical Analysis",,,Wm. C. Brown,Dubuque Iowa,1988,,,,1,,

s2ab3,7,14,18,,,,Aberth O.,,,"Precision Numerical Analysis",,,Wm. C. Brown,Dubuque Iowa,1988,,,,1,,

s2ab4,2,14,18,,,,Aberth O.,,,"Precise Numerical Methods using C++",,,Academic Press,,1998,,,,1,,

s2ab5,26,,,,,,Aberth O.,,,"Precise Numerical Methods using C++",,,Academic Press,,1998,,,,1,,

s2ab6,25,,,,,,Adamson I.T.,,,"Introduction to Field Theory",,,Wiley,New York,1964,,,,1,,

s2ab7,31,,,,,,Agardh C.A.,,,"Sur une méthode élémentaire de résoudre les équations numériques d'un degré quelqonque par la sommation des Series",,,,Carlstad,1847,,,,1,,

,19,0,0,0,0,0,Hofmann J.E.,,,Michael Stifel 1487?-1567. Leben, Wirken, und Bedeutung für die Mathematik seiner Zeit.,,,F. Steiner,Wiesbaden,1968,0,0,Considers geometrical solution of quadratic.,1,0,

,20,29,0,0,0,0,Dynkin E.B.,Uspenskii V.A.,,Problems in the Theory of Numbers, Part Two of Mathematical Conversations.,,,D.C. Heath and Co.,,1963,0,0,,1,0,

s2mj82,29,,,,,,Müller C.,,,Wie fand Archimedes die von ihm gegebenen Näherungswerte von $\sqrt{3}$ ?,Quel. Stud. Gesch. Math. Astr. Phys. Ser. B,2,,,1930,281,285,,1,,

s2mj83,31,,,,,,Murphy R.,,,On the Resolution of Algebraic Equations,Trans. Cambridge Philos. Soc.,4,,,1819,125,153,,1,,

s2mj84,13,19,,,,,Murphy R.,,,Analysis of the Roots of Equations,Philos. Trans. Roy. Soc. London,127,,,1837,161,178,,1,,

s2mb1,29,,,,,,Maccaferri E.,,,"Calcolo numerico approssimato",,,Hoepli,Milan,1919,,,,1,,

s2mb2,20,,,,,,Macwilliams F.,Sloane N.J.A.,,"The Theory of Error- Correcting Codes Vol.1",,,North-Holland,Amsterdam,1976,,,,1,,

s2mb3,29,,,,,,Majerski S.,,,Square-root algorithms for high-speed digital circuits in "Proc. 6th IEEE Symposium on Computer Arithmetic",,,,,1983,99,102,,1,,

s2mb4,2,,,,,,Maseres F.,,,On Mr. Raphson's Method of Resolving Affected Equations by Approximation in "Bernoulli's Mathematical Tracts",,,,London,1795,577,586,,1,,

s2mb5,20,,,,,,Mathews G.B.,,,"Theory of Numbers",,,,Cambridge,1892,,,,1,,

s2mb6,19,25,,,,,Mathews G.B.,,,"Algebraic Equations",,,,Cambridge,1907,,,,1,,

s2mb7,13,19,,,,,Matthiessen L.,,,"Die algebraischen Methoden der Auflösung der litteralen quadratischen cubischen und biquadratischen Gleichungen",,,,Leipzig,1866,,,,1,,

s2mb8,19,,,,,,Matthiessen L.,,,"Grundzüge der antiken und modernen Algebra",,,B.G. Teubner,Leipzig,1896,,,,1,,

s2mb9,5,13,,,,,Maurin K.,,,Solution of an arbitrary algebraic equation by means of a theta function (in Polish) in "Leksykon Matematyczny" M. Kordosa et al eds.,,,Wiedza Powszechna,Warsaw,1993,906,910,,1,,

s2mb10,10,,,,,,Maza M.M.,Rioboo R.,,Polynomial GCD Computations over Towers of Algebraic Extensions in "Applied Algebra; Algebraic Algorithms and Error-Correcting Codes" G. Cohen et al Eds.,,,Springer-Verlag,,1995,365,382,,1,,

s2mb11,1,2,7,,,,McCalla T.R.,,,"Introduction to Numerical Methods and FORTRAN Programming",,,Wiley,New York,1967,,,,1,,

s2mb12,1,2,7,17,,,McCormick J.M.,Salvadori M.G.,,"Numerical Methods in Fortran",,,Prentice-Hall,Englewood Cliffs NJ,1964,,,,1,,

s2mb13,20,,,,,,McEliece R.J.,,,"Finite Fields for Computer Scientists and Engineers",,,Kluwer Academic Publisher,,1987,,,,1,,

s2mb14,29,,,,,,McQuillan S.E.,McCanny J.V.,,A VLSI architecture for multiplication division and square root in "Proc. 1991 International Conference on Acoustics Speech and Signal Processing",,,IEEE,,1991,1205,1208,,1,,

s2mb15,29,,,,,,McQuillan S.E.,McCanny J.V.,Hamill R.,New algorithms and VLSI architectures for SRT division and square root in "Proc. 11th IEEE Symposium on Computer Arithmetic",,,IEEE,,1993,80,86,,1,,

s2mb16,20,,,,,,Menezes A.J. et al (eds.),,,"Applications of Finite Fields Chap. 2",,,Kluwer,Dordrecht,1993,,,,1,,

s2mb17,19,,,,,,Mikami Y.,,,"The Developement of Mathematics in China and Japan",,,,Leipzig,1913,,,,1,,

s2mb18,19,25,,,,,Miller G.A.,Blichfeldt H.F.,Dickson L.E.,"Theory and Applications of Finite Groups",,,Dover,,1961,,,,1,,

s2mb19,13,,,,,,Miller V.S.,,,Factoring polynomials via relation-finding in "Theory of Computing and Systems; LNCS 601" eds. D. Dolev Z. Galil and M. Rodeh,,,Springer-Verlag,New York,1992,115,121,,1,,

s2mb20,18,19,28,,,,Milovanovi\'{c} G.V.,Mitrovini\'{c} D.S.,Rassias M. Th.,"Topics in Polynomials: Extremal Problems; Inequalities; Zeros",,,World Scientific,Singapore,1994,,,,1,,

s2mb21,10,18,,,,,Mishra B.,,,"Algorithmic Algebra",,,Springer-Verlag,,1993,,,,1,,

s2mb22,7,,,,,,Möbius A.F.,,,Beitrag zur Lehre von der Auflösung numerischer Gleichungen in "Gesammelte Werke Vol. 4",,,,Leipzig,1887,381,386,,1,,

s2mb23,19,,,,,,Montucla J.E.,,,"Histoire des Mathématiques",,,H. Agasse,Paris,1802,,,,1,,

s2mb24,29,,,,,,Montuschi P.,Ciminiera L.,,Simple radix 2 division and square root with skipping of some addition steps in "Proc. 10th IEEE Symposium on Computer Arithmetic",,,,,1991,202,209,,1,,

s2mb25,10,20,,,,,Moses J.,,,The Evolution of Algebraic Manipulation Algorithms in "1975 Best Computer Papers" I.L. Auerbach Ed.,,,Petrocelli,New York,1975,197,214,,1,,

s2mb26,20,,,,,,Moses J.,,,Algebraic Structures and their Algorithms in "Algorithms and Complexity" ed. J.F. Traub,,,,,1976,301,319,,1,,

s2mb27,19,29,,,,,Müller J.H.T.,,,"Lehrbuch der Mathematik",,,,Halle,1838,,,,1,,

s2mb28,2,10,18,19,29,31,Murphy R.,,,"A Treatise on the Theory of Algebraical Equations",,,,London,1839,,,,1,,

s2nj1,13,,,,,,Naegelsbach H.,,,Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten,Arch. Math. Phys.,59,,,1876,147,192,,1,,

s2nj2,28,,,,,,Sz.-Nagy J.v.,,,über algebraische Gleichungen mit lauter Wurzeln,Jahresber. Deutsch. Math.-Verein.,27,,,1918,37,43,,1,,

s2nj3,20,,,,,,Naudin P.,Quittí C.,,Univariate polynomial factorization over finite fields (Tutorial),Theoret. Comput. Sci.,191,,,1998,1,36,,1,,

s2nj4,13,,,,,,Neff C.A.,Reif J.H.,,An Efficient Algorithm for the Complex Roots Problem,J. Complexity,12,,,1996,81,115,,1,,

s2nj5,21,,,,,,Nell A.M.,,,Die Auflösung dreigliedriger Gleichungen nach Gauss,Arch. Math. Phys. Ser. 2,1,,,1884,311,333,,1,,

s2nj6,19,,,,,,Neugebauer O.,,,Arithmetik und Rechentechnik der ägypter,Quel. Stud. Gesch. Math. Astr. Phys. Ser. B,1,,,1930,306,311,,1,,

s2nj7,19,,,,,,Neugebauer O.,,,Studien zur Geschichte der Antiken Algebra,Quel. Stud. Gesch. Math. Astr. Phys. Ser. B,2,,,1932,1,27,,1,,

s2nb10,19,29,,,,,Neugebauer O.,,,"The Exact Sciences in Antiquity 2/Ed.",,,Brown U.P.,Providence,1957,,,Babylonian surds and quadratics,1,,

s2nb11,29,,,,,,Neugebauer O.,,,"Mathematical Cunieform Texts",,,Oriental Society,New Haven,1986,,,,1,,

s2nb12,2,,,,,,Newton I.,,,"The correspondence of Isaac Newton Vol. 1"; ed. H.W. Turnbull,,,,Cambridge,1959,309,310,,1,,

s2nb13,2,,,,,,Nicholson J.W.,,,"A Direct and General Method of Finding the Approximate Values of the Real Roots of Numerical Equations to any Degree of Accuracy",,,F.F. Hansell,New Orleans,1891,,,,1,,

s2nb14,20,,,,,,Niederreiter H.,,,New deterministic factorization algorithms for polynomials over finite fields in "Intern. Conf. on Finite Fields; G.L. Mullen et al Eds.,,,Amer. Math. Soc.,,1994,251,268,,1,,

s2nb15,16,,,,,,Novak E.,,,Algorithms and complexity for continuous problems in "Geometry Analysis and Mechanics",,,World Scientific,Singapore,1994,157,188,,1,,

s2nb16,1,2,7,,,,Novak E.,,,The Bayesian Approach to Numerical Problems: Results for Zero-Finding in "Numerical Methods and Error Bounds" eds. G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,164,171,,1,,

s2oj1,11,,,,,,Obreshkoff N.,,,über die Wurzeln von algebraischen Gleichungen,Jahresber. Deutsch. Math.-Verein.,33,,,1924,52,64,,1,,

s2oj2,11,,,,,,Obreshkoff N.,,,über die Trennung der reellen Wurzeln von algebraischen Gleichungen,Jahresber. Deutsch. Math.-Verein.,37,,,1928,234,237,,1,,

s2oj3,2,,,,,,Ocken S.,,,Convergence Criteria for Attracting Cycles of Newton's Method,SIAM J. Appl. Math.,58,,,1998,235,244,,1,,

s2oj4,27,,,,,,Odlyzko A.M.,Poonen B.,,Zeros of polynomials with 0/1 coefficients,Enseign. Math.,39,,,1993,317,348,,1,,

s2oj5,13,,,,,,Olivier L.,,,Ein kennzeichen der Grenzen der Zahl der reellen Wurzeln einer beliebigen algebraischen Gleichung,J. Reine Angew. Math.,1,,,1826,223,227,,1,,

s2oj6,13,,,,,,Olivier L.,,,Anwendung der Interpolations-Formeln auf die Auflösung der algebraischen Gleichungen von beliebigen Graden,J. Reine Angew. Math.,2,,,1827,214,216,,1,,

s2oj7,20,29,,,,,Oltramare,,,Considérations sur les racines des nombres premiers,J. Reine Angew. Math,45,,,1853,303,344,,1,,

s2oj8,15,,,,,,Orchard H.J.,,,The Laguerre method for finding the zeros of polynomials,IEEE Trans. Circuits and Systems,36,,,1989,1377,1381,,1,,

s2oj9,15,,,,,,Osada N.,,,Improving the order of convergence of iteration functions,J. Comp. Appl. Math,98,,,1998,311,315,,1,,

s2oj10,17,,,,,,Overill R.E.,,,On the rapid parallel evaluation of power series,Supercomputer,8 No. 4,,,1991,38,41,,1,,

s2oj11,17,,,,,,Overill R.E.,Wilson S.,,Data parallel evaluation of univariate polynomials by the Knuth-Eves algorithm,Parallel Comput.,23,,,1997,2115,2127,,1,,

s2ob1,12,15,,,,,Oliveira F.A.,,,Bounding solutions of non-linear equations with interval analysis in "IMACS '91" ed. R. Vichnevetsky and J.J.H. Miller,,,,,1991,246,247,,1,,

s2pj1,11,,,,,,Pal D.,Kailath T.,,Displacement structure approach to singular root distribution problems: The imaginary axis case,IEEE Trans. Circuits and Systems I,41,,,1994,138,148,,1,,

s2lb20,10,,,,,,Lockhart J.,,,"Extension of the celebrated theorem of C. Sturm",,,,Oxford,1839,,,,1,,

s2lb21,18,,,,,,Lockhart J.,,,"Resolution of Equations by means of Inferior and Superior Limits",,,,London,1842,,,,1,,

s2lb22,10,18,,,,,Lockhart J.,,,"The Nature of the Roots of Numerical Equations",,,,London,1850,,,,1,,

s2lb23,2,13,19,,,,Lockhart J.,Weddle T.,Rutherford W.,"Resolution of Equations",,,,Oxford,1837,,,,1,,

s2lb24,10,,,,,,Lombardi H.,,,Sous-Resultants; Suite de Sturm; Specialization in "Publications Mathematiques de la Faculté de Science de Besancon Vol 2: Theorie des nombres",,,,,1988,,,,1,,

s2lb25,19,29,,,,,Loria G.,,,"Le scienze esatte nell'antic Grecia",,,,Milan,1914,845,919,,1,,

s2lb26,13,19,25,,,,Loria G.,,,"Storia delle matematiche Vols 1/2/3",,,,Turin,1929,,,,1,,

s2lb27,29,,,,,,Lu P.Y.,Duwallu K.,,A VLSI module for IEEE floating-point multiplication/division/square root in "Proc. of the IEEE International Conference on Computer Design: VLSI in Computers and Processors",,,IEEE,,1989,366,368,,1,,

s2lb28,21,,,,,,Lubinsky D.,,,Zeros of orthogonal and biorthogonal polynomials: some old; some new in "Nonlinear Numerical methods and Rational Approximation II" ed. A. Cuyt,,,Kluwer,Dordrecht,1994,3,16,,1,,

s2lb29,7,19,29,,,,Lüroth J.,,,"Vorlesungen über numerisches Rechnen",,,,Leipzig,1900,,,,1,,

s2mj1,7,,,,,,Maas C.,,,Was ist das Falsche an der Regula Falsi?,Mitteilungen der mathematische Gesselschaft in Ham,B11 (3),,,1985,311,317,,1,,

s2mj2,20,,,,,,Maclean K.R.,,,Prime-valued polynomials,Math. Gaz.,82,,,1998,195,202,,1,,

s2mj3,29,,,,,,Macmillan P.,,,Roots from Square Roots,Math. Gaz.,79,,,1995,353,354,,1,,

s2mj4,1,2,3,6,7,10,Maeder A.J.,Wynton S.A.,,Some parallel methods for polynomial root finding,J. Comput. Appl. Math.,18,,,1987,71,81,,1,,

s2mj5,14,,,,,,Maeder A.J.,Wynton S.A.,,Some parallel methods for polynomial root finding,J. Comput. Appl. Math.,18,,,1987,71,81,,1,,

s2mj6,18,,,,,,Mahler K.,,,A remark on a paper of mine on polynomials,Illinois J. Math.,8,,,1964,1,4,,1,,

s2mj7,29,,,,,,Majithia J.C.,,,Cellular array for extraction of squares and square roots of binary numbers,IEEE Trans. Comput.,21,,,1972,1023,1024,,1,,

s2mj8,29,,,,,,Majithia J.C.,,,Pipeline array for square root extraction,Electron. Lett.,9 No. 1,,,1973,4,5,,1,,

s2mj9,29,,,,,,Majithia J.C.,Kitai R.,,A cellular array for the non-restoring extraction of square roots,IEEE Trans. Comput.,20,,,1971,1617,1618,,1,,

s2mj10,3,,,,,,Makrelov E.V. et al,,,Method for the simultaneous finding... (Russian),Serdica,12,,,1986,351,357,,1,,

s2ab10,22,,,,,,Akritas A.G.,,,"Elements of Computer Algebra with Applications",,,John Wiley and Sons,New York,1989,,,,1,,

s2ab12,19,,,,,,Al-Kharizmi,,,"Kitab al Mukhtasarfi Hisab al Jabr wa'l Muqabala" ed F.Rosen,,,,London,1830,,,,1,,

s2ab13,19,,,,,,Al-Tusi,,,"Oeuvres mathematiques. Algèbre et géométrie au XIIe siècle vol 2" ed. R. Rashed,,,,Paris,1986,,,,1,,

s2ab15,20,,,,,,Arnoux G.,,,"Arithmetique Graphique",,,Gauthier-Villars,Paris,1906,,,,1,,

s2ab16,25,,,,,,Artin E.,,,"Foundations of Galois Theory Lectures at New York University",,,New York University,,1938,,,,1,,

s2ab17,22,25,,,,,Artin E.,,,"Modern Higher Algebra: Galois Theory",,,NYU-Courant Institute of ,New York,1947,,,,1,,

s2ab18,29,,,,,,Aryabhata,,,"Aryabhatiya of Aryabhata" Trans. K.S. Shukla,,,Indian National Academy o,New Delhi,1976,36,37,,1,,

s2ab20,2,3,5,,,,Atanassova L.,Andreev A.,Kjurkchiev N.,Combined iterative methods based on a modification of the Koenig theorem in "Numerical Methods and Error Bounds" ed. G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,23,37,,1,,

s2ab21,3,12,,,,,Atanassova L.Y.,Herzberger J.P.,,A unified approach to some classes of simultaneous inclusion methods for polynomial zeros in "World Congress of Nonlinear Analysts '92" ed V. Lakshmikantham,,,Walter de Gruyter,Berlin,1995,3897,3906,,1,,

s2mj76,29,,,,,,Montuschi P.,Ciminiera L.,,Reducing iteration time when result digit is zero for radix-2 SRT division and square root with redundant remainders,IEEE Trans. Comput.,42,,,1993,239,246,,1,,

s2mj77,19,25,,,,,Moore E.H.,,,Concerning the general equations of the seventh and eighth degrees,Math. Ann.,51,,,1899,417,444,,1,,

s2mj78,20,,,,,,Moreno O.,,,On primitive elements of trace equal to 1 in GF(2^m),Discrete Math.,41,,,1982,53,56,,1,,

s2mj79,20,,,,,,Moreno O.,,,On the existence of a primitive quadratic of trace over GF(2^p),J. of Combinatorial Theory,A51,,,1989,104,110,,1,,

s2mj80,20,,,,,,Morgan I.H.,Mullen G.L.,,Primitive normal polynomials over finite fields,Math. Comp.,63,,,1994,759,765,,1,,

s2mj81,21,26,,,,,Mossinghoff M.J.,Pinner C.G.,Vaaler J.D.,Perturbing polynomials with all their roots on the unit circle,Math. Comp.,67,,,1998,1707,1726,,1,,

s2nj8,21,,,,,,Nevai P.G.,Dehesa J.S.,,On asymptotic average properties of zeros of orthogonal polynomials,SIAM J. Math. Anal.,10,,,1979,1184,1192,,1,,

s2nj9,10,13,,,,,Newman H.,Pao Y.C.,,Factorization of Polynomials Based on the Multiplicities of their Roots and Applications,Comput. Math. Appl.,32 (9),,,1996,29,40,,1,,

s2nj10,19,,,,,,Nickalls R.W.D.,,,A note on solving cubics,Math. Gaz.,80,,,1996,576,577,,1,,

s2nj11,18,,,,,,Nickalls R.W.D.,Dye R.H.,,The geometry of the discriminant of a polynomial,Math. Gaz.,80,,,1996,279,285,,1,,

s2nj12,20,,,,,,Niederreiter H.,Göttfert R.,,Factorization of polynomials over finite fields and characteristic sequences,J. Symb. Comput.,16,,,1993,401,412,,1,,

s2nj13,20,,,,,,Niederreiter H.,Göttfert R.,,On a new factorization algorithm for polynomials over finite fields,Math. Comp.,64,,,1995,347,353,,1,,

s2nj14,1,16,,,,,Nievergelt Y.,,,Bisection hardly ever converges linearly,Num. Math.,70,,,1995,111,118,,1,,

s2nj15,17,,,,,,Novak E.,,,The real number model in numerical analysis,J. Complexity,11,,,1995,57,73,,1,,

s2nj16,1,16,,,,,Novak E.,,,Topological Complexity of Zero-Finding,J. Complexity,12,,,1996,380,400,,1,,

s2nj17,1,2,16,,,,Novak E.,Ritter K.,,Some complexity results for zero finding for univariate functions,J. Complexity,9,,,1993,15,40,,1,,

s2nj18,1,7,,,,,Novak E.,Ritter K.,Wozniakowski H.,Average-Case Optimality of a Hybrid Secant-Bisection Method,Math. Comp.,64,,,1995,1517,1539,,1,,

s2nb1,25,,,,,,Nagata M.,,,"Field Theory",,,Marcel Dekker,New York,1977,,,,1,,

s2nb2,20,,,,,,Nagell T.,,,"Introduction to Number Theory",,,Chelsea,,1964,,,,1,,

s2nb3,21,,,,,,Natanson I.P.,,,"Constructive Function Theory Vol. III",,,Frederick Ungar,New York,1965,,,,1,,

s2nb4,13,,,,,,Neff C.A.,Reif J.H.,,An 0(n^1+ε log(b)) algorithm for the complex root problem in "Proc. 35th Annual IEEE Symp. on Foundations of Computer Science",,,IEEE Computer Science Pre,,1994,540,547,,1,,

s2nb5,19,,,,,,Nesselmann G.H.F.,,,"Die Algebra der Griechen",,,Reimer,Berlin,1842,,,,1,,

s2nb6,19,,,,,,Nesselmann G.H.F.,,,"Versuch einer kritischen Geschichte der Algebra der Griechen",,,,Berlin,1847,,,,1,,

s2nb7,19,21,25,,,,Netto E.,,,"The Theory of Substitutions and its Applications to Algebra; trans. F.N. Cole,,,Chelsea,New York,1964,,,,1,,

s2nb8,10,19,,,,,Neuberg J.,,,"Cours d'Algèbre Supérieure",,,A. Herman,Paris,1909,,,,1,,

s2nb9,19,29,,,,,Neugebauer O.,,,"Vorlesungen über die Geschichte der antiken Mathematik Vol. 1",,,Springer-Verlag,,1934,,,,1,,

,19,0,0,0,0,0,Tropfke J.,,,Zur Geschichte d. quadratischen Gleichungen uber dreieinhalb Jahrtausende,Jahresber. Deutsch. Math.-Verein,44,,,1934,26,47,Early treatment of quadratic,1,0,

,7,0,0,0,0,0,Wu X.,Fu D.,,New High-order convergence iteration methods without employing derivatives for solving nonlinear equations,Comput. Math. Appl.,41,,,2001,489,495,Not more efficient than Newton, uses f(x_n - f(x_n)),1,0,

,29,0,0,0,0,0,Woepcke, F.,,,Recherches sur l'histoire des sciences mathématiques chez les orientaux,J. Asiatique (5 ser.),4,,,1854,348,384,Gives continued fraction for square root,1,0,

,29,0,0,0,0,0,Boncompagni,Moret-Blanc, B.,,Question 1111,Nouv. Ann. Math. (2 ser.),12,,,1873,191,192,See also pp 477-480,1,0,

,19,0,0,0,0,0,Sédillot L,,,Matériaux pour servir àl'histoire comparée des sciences mathématiques chez les Grecs et les orientaux,,,,Paris,1845,447,447,Arabic treatment of cubic,1,0,

,29,0,0,0,0,0,Bailey, V.A.,,,Prodigious Calculation,Austr. J. of Sci.,3,,,1941,78,80,Describes efficient method for roots.,1,0,

,29,0,0,0,0,0,Grant, J.A.,Mir, N.A.,,A Numerical Comparison of Methods for Finding Simultaneously all the Zeros of a Real Polynomial,Reports on Numerical Analysis No NA 93-36,,,Bradford, Yorkshire,1994,0,0,Six methods related to Durand-Kerner and Ehrlich methods are compared. Modified Improved Ehrlich method is best.,1,0,

,4,0,0,0,0,0,Malajovich, G.,Zubelli, J.P.,,Tangent Graeffe Iteration,Numer. Math.,89,,,2001,749,,A variation of Graeffe iteration is described, suitable for floating-point arithmetic.,1,0,

,19,0,0,0,0,0,Kalman, D.,White, J.E.,,Polynomial Equations and Circulant Matrices,Amer. Math. Monthly,108,,,2001,821,840,Unifies treatment of low-degree polynomials.,1,0,

,19,29,0,0,0,0,Lam, L.Y.,,,A Critical Study of the Yang Hui Suan Fa, a Thirteenth Century Math. Treatise,Singapore Univ. Press,,,,1977,0,0,Quadratics and square roots in medieval China,1,0,

,29,0,0,0,0,0,Wertheim, G.,,,Die Arithmetik des Elia Misrachi,,,Braunschweig,,1896,0,0,Early treatment of squiare and cube roots,1,0,

,19,29,0,0,0,0,Ho Peng Yoke,,,Article on Chu Shih-chieh.,Dict. Sci. Biog.,3,Scribner's,New York,1970,265,271,Chinese author used Horner's method to solve low degree polynomials and square roots.,1,0,

,10,0,0,0,0,0,Lang, S.,,,Undergraduate Algebra, 2nd ed.,,,Addison-Wesley,Menlo Pk, Calif,1984,0,0,Treats GCD,1,0,

,2,0,0,0,0,0,Wu X.Y.,,,A new continuation Newton-like method and its deformation,Appl. Math. Comput.,112,,,2000,75,78,Considers variation on Newton's method where f' is replaced by qf+f'.,1,0,

,29,0,0,0,0,0,Vogel, Kurt,,,Chiu Chang Suan Shu: Neun Bucher arithmetischer Technik: Ein Chinesiches Rechenbuch fur den praktischen Gebrauch aus der fruhen Hanzeit,,,Braunschweig,,1968,0,0,Early Chinese treatment of square and cube roots.,1,0,

,19,0,0,0,0,0,Struik D.J.,,,"Omar Khayyam, Mathematician.",Math. Teacher,51,,,1958,280,285,Brief mention of cubics.,1,0,

s2pj2,21,,,,,,Pan K.,Saff E.B.,,Asymptotics for zeros of Szëgo polynomials associated with trigonometric polynomial signals,J. Approx. Theory,71,,,1992,239,251,,1,,

s2pj3,17,,,,,,Pan V.Y.,,,Fast Evaluation and Interpolation at the Chebyshev Sets of Points,Appl. Math. Lett.,2,,,1989,255,258,,1,,

s2pj4,17,,,,,,Pan V.Y.,,,An Algebraic Approach to Approximate Evaluation of a Polynomial on a Set of Real Points,Advances in Computational Math.,3,,,1995,41,58,,1,,

s2pj5,5,10,,,,,Pan V.Y.,,,Deterministic Improvement of Complex Polynomial Factorization Based on the Properties of the Associated Resultant,Comput. Math. Appl.,30 No. 2,,,1995,71,94,,1,,

s2pj6,5,,,,,,Pan V.Y.,,,Optimal and Nearly Optimal Algorithms for Approximating Polynomial Zeros,Comput. Math. Appl.,31 (12),,,1996,97,138,,1,,

s2pj7,30,,,,,,Pan V.Y.,,,Faster computing xⁿ mod p(x) and an application to splitting a polynomial into factors over a fixed disc,J. Symbolic Comput.,22,,,1996,377,380,,1,,

s2pj8,10,,,,,,Pan V.Y.,,,Parallel computation of polynomial GCD and some related parallel computations over abstract fields,Theoret. Comput. Sci.,162,,,1996,173,224,,1,,

s2pj9,1,,,,,,Pan V.Y.,,,Solving a Polynomial Equation: Some History and Recent Progress,SIAM Rev.,39,,,1997,187,220,,1,,

s2pj10,1,2,5,,,,Pan V.Y.,,,Solving Polynomials with Computers,American Scientist,86 No. 1,,,1998,62,69,,1,,

s2pj11,17,,,,,,Pan V.Y.,,,New Fast Algorithms for Polynomial Interpolation and Evaluation on the Chebyshev Node Set,Comput. Math. Appl.,35 No. 3,,,1998,125,129,,1,,

s2pj12,13,,,,,,Pan V.Y. et al,,,On Isolation of Real and Nearly Real Zeros of a Univariate Polynomial and Its Splitting into Factors,J. Complexity,12,,,1996,572,594,,1,,

s2pj13,19,,,,,,Pan V.Y. et al,,,Fast multipoint polynomial evaluation and interpolation via computations with structured matrices,Ann. Numer. Math,4,,,1997,483,510,,1,,

s2pj14,17,,,,,,Pan V.Y. et al,,,A new approach to fast polynomial interpolation and multipoint evaluation,Comput. Math. Appl.,25 No. 9,,,1993,25,30,,1,,

s2pj15,14,,,,,,Pao Y.C.,Newman M.,,A Direct Algorithm for Extracting a Transfer Function's Multiple Zeroes or Poles,Comput. Math. Applic.,35 No.9,,,1998,33,44,,1,,

s2pj16,21,,,,,,Peherstorfer F.,,,A partial solution to a problem,J. Comput. Appl. Math.,48,,,1993,241,243,,1,,

s2pj17,20,,,,,,Peherstorfer F.,Schmuckenschläger M.,,Interlacing properties of zeros of associated polynomials,J. Comput. Appl. Math.,59,,,1995,61,78,,1,,

s2pj18,20,,,,,,Pellet A.,,,Sur la décomposition d'une fonction entière en facteurs irréductibles suivant une module premier p,C.R. Acad. Sci. Paris,86,,,1878,1071,1072,,1,,

s2pj19,13,,,,,,Pellet A.,,,Calcul des racines reélles des équations,C.R. Acad. Sci. Paris,133,,,1901,1186,1186,,1,,

s2pj20,2,13,,,,,Pellet A.,,,Sur la formule d'approximation de Newton,Bull. Soc. Math. France,29,,,1901,139,142,,1,,

s2pj21,2,,,,,,Pellet A.,,,Approximation des racine des équations,Assoc. Franc. pour l'avancement des Sciences,31,,,1902,166,171,,1,,

s2pj22,21,,,,,,Pérez T.E.,Piñar M.A.,,Global properties of zeros of Sobolev-type orthogonal polynomials,J. Comput. Appl. Math.,49,,,1993,225,232,,1,,

s2pj23,7,18,,,,,Perrin R.,,,Sur la séparation et le calcul des racines réelles des équations,C.R. Acad. Sci. Paris,133,,,1901,1189,1189,,1,,

s2pj24,18,,,,,,Perrin R.,,,Sur un critérium de l'existence des racines réelles d'un équation numérique dans un intervalle donné,Assoc. Franc. pour l'avancement des Sciences,31,,,1902,178,185,,1,,

s2pj25,20,,,,,,Petersen E.L.,,,Eine Bedingungen für die irreduziblen Faktoren von gewissen Polynome modulo eines Primzahlprodukts,Jber. Deutsche Math.-Verein.,45,,,1935,169,172,,1,,

s2pj26,20,,,,,,Petersen E.L.,,,über einen Satz von O. öre,J. Reine Angew. Math.,172,,,1935,217,218,,1,,

s2pj27,3,,,,,,Petkovi\'{c} M.S.,,,On Initial Conditions for the Convergence of Simultaneous Root Finding Methods,Computing,57,,,1996,163,177,,1,,

s2pj28,3,,,,,,Petkovi\'{c} M.S.,Carstensen C.,Trajkovi\'{c} M.,Weierstrass formula and zero-finding methods,Numer. Math.,69,,,1995,353,372,,1,,

s2pj29,3,,,,,,Petkovi\'{c} M.S.,Herceg D.D.,,On the convergence of the Wang-Zheng's method,J. Comput. Appl. Math.,91,,,1998,123,135,,1,,

s2pj30,3,,,,,,Petkovi\'{c} M.,Herceg D.,Ili\'{c} S.,Point estimation and some applications to iterative methods,BIT,38,,,1998,112,126,,1,,

s2pj31,3,,,,,,Petkovi\'{c} M.S.,Herceg D.,Ili\'{c} S.,Safe convergence of simultaneous methods for polynomial zeroes,Numerical Algorithms,17,,,1998,313,331,,1,,

s2pj32,3,,,,,,Petkovi\'{c} M.S.,Ili\'{c} S.,Tri\v{c}kovi\'{c} S.,A Family of Simultaneous Zero-Finding Methods,Comput. Math. Appl.,34 No. 10,,,1997,49,59,,1,,

s2pj33,3,,,,,,Petkovi\'{c} M.S.,Kjurkchiev N.,,A note on the convergence of the Weierstrass SOR method for polynomial roots,J. Comput. Appl. Math.,80,,,1997,163,168,,1,,

s2pj34,3,12,18,,,,Petkovi\'{c} M.,Mignotte M.,Trajkovi\'{c} M.,The Root Separation of Polynomials and Some Applications,Z. Angew. Math. Mech.,75,,,1995,551,561,,1,,

s2pj35,3,,,,,,Petkovi\'{c} M.S.,Petkovi\'{c} L.D.,Herceg D.D.,Point Estimation of a Family of Simultaneous Zero-Finding Methods,Comput. Math. Appl.,36 No. 2,,,1998,1,12,,1,,

s2pj36,15,,,,,,Petkovi\'{c} M.S.,Tri\v{c}kovi\'{c} S.,,On zero-finding methods of the fourth order (Letter),J. Comput. Appl. Math.,64,,,1995,291,294,,1,,

s2pj37,3,,,,,,Petkovi\'{c} M.S.,Tri\v{c}ovi\'{c} S.B.,,Tchebychef-Like method for the Simultaneous Finding Zeros of Analytic Functions,Comput. Math. Appl.,31 No. 8,,,1996,85,93,,1,,

s2pj38,25,,,,,,Pierpont J.,,,Lagrange's place in the theory of substitutions,Bull. Amer. Math. Soc.,1,,,1895,196,204,,1,,

,20,0,0,0,0,0,Reid, L.W.,,,The Elements of the Theory of Algebraic Numbers,,,Macmillan,New York,1910,0,0,Treats congruences,1,0,

,19,0,0,0,0,0,Bruins, E.M.,,,Interpretaion of Cunieform Mathematics,Physis,4,,,1962,277,341,Babylonian quadratics,1,0,

,19,0,0,0,0,0,Curtze, M.,,,Commentar zu dem 'Tractatus de numeris datis' des Jordanus Neomorarius,Zeit. Math. Phys. Hist.-lit.Abtg.,36,,,1891,1,23,also pp41-63,81-95,121-138. Medieval quadratics,1,0,

,19,0,0,0,0,0,Hughes, B.B.,,,Johann Scheubel's Revision of Jordanus de Nemore's "De Numeris Datis": An Analysis of an Unpublished Manuscript,Isis,63,,,1972,221,234,Treat quadratics,1,0,

,13,19,0,0,0,0,Lagrange, J.L.,,,Lectures on Elementary Mathematics, trans T.J. McCormack,,,Kegan Paul,London,1898,96,0,Treats cubic, biquadratic, and general case,1,0,

,19,0,0,0,0,0,Karpinski, L.C.,,,Algebraic Works to 1700,Scripta Math,10,,,1944,145,169,History of quadratic and cubic,1,0,

,2,12,0,0,0,0,Petkovic, L.D.,Trickovic, S.,Petkovic, M.,Slope Methods of Higher Order for the Inclusion of Complex Roots of Polynomials,Reliable Computing,3,,,1997,349,362,Combining the Newton method with the interval slope, two new algorithms of higher order in circular complex arithmetic are developed.,1,0,

,3,0,0,0,0,0,Trickovic, S.,Trajkovic, M.,Petkovic, M.,Asynchronous Methods for Simultaneous Determination of Polynomial Roots,Filomat,9,,,1995,273,284,Considers simultaneous methods for the determination of polynomial roots on a distributed memory multicomputer.,1,0,

,19,0,0,0,0,0,Kline, Morris,,,Mathematics: A Cultural Approach,,,Addison-Wesley,Reading. Mass.,1962,12,,Treats quadratic & (briefly) cubic,1,0,

,20,0,0,0,0,0,Stein, G.,,,Factoring cyclotomic polynomials over large finite fields, in "Finite Fields and Applications", eds S. Cohen and H. Niederreiter,,,Cambridge Univ Press,,1996,349,354,,1,0,

,1,2,7,14,15,24,Mathews, J.H.,,,Numerical Methods for Computer Science, Engineering and Mathematics,,,Prentice-Hall Inc.,Englewood Clfs, N.J.,1987,0,0,Covers bisection, Newton, secant, Muller, Bairstow, acceleration,1,0,

,20,0,0,0,0,0,Von zur Gathen, J.,Panario, D.,,Factoring polynomials over finite fields: a survey,J. Symb. Comput.,31 1/2,,,2001,3,17,Title says it.,1,0,

,10,20,0,0,0,0,Wang, P.S.,,,Parallel Polynomial Operations on SMPs; an Overview,J. Symb. Comput.,21,,,1996,397,410,Covers GCD and factoring modulo small primes.,1,0,

,10,0,0,0,0,0,Corless, R.,,,Cofactor iteration,ACM SIGSAM Bull.,30 No. 1,,,1996,34,38,Finds best GCD of approximate polynomials.,1,0,

,10,0,0,0,0,0,Noda, M.-T.,Sasaki, T.,,Approximate GCD and its application to ill-conditioned algebraic equations,J. Comput. Appl. Math.,38,,,1991,335,351,Applies GCD to separating multiple or close roots.,1,0,

,19,29,0,0,0,0,Al-Daffa, A.A.,,,The Muslim Contribution to Mathematics,,,Humanities Press,Atl Highlands, N.J.,1977,0,0,Early treatment of quadratics and square roots.,1,0,

s2pj39,25,,,,,,Pierpont J.,,,Galois' Theory of Algebraic Equations,Ann. Math. Ser. 2,1,,,1899,113,143,see also ibid vol 2 pp22-55,1,,

s2pj40,25,,,,,,Pierpont J.,,,Early History of Galois' Theory of Equations,Bull. Amer. Math. Soc. Ser. 2,4,,,1898,332,340,,1,,

s2pj41,13,,,,,,Pietrus A.,,,A globally convergent method for solving non-linear equations without the differentiability condition,Numerical Algorithms,13,,,1996,61,76,,1,,

s2pj42,20,29,,,,,Pila J.,,,Frobenius maps of abelian varieties and finding roots of unity in finite fields,Math. Comput.,55,,,1990,745,763,,1,,

s2pj43,21,,,,,,Piobert,,,Méthodes pour trouver les valeurs approchées des racines réelles des équations algébriques,Nouv. Ann. Math.,10,,,1851,175,180,,1,,

s2pj44,20,29,,,,,Pocklington H.C.,,,The Direct Solution of the Quadratic and Cubic Binomial Congruences with Prime Moduli,Proc. Cambridge Philos. Soc,19,,,1917,57,59,,1,,

s2sj1,20,21,,,,,Saff E.B.,Varga R.S.,,Zero-free parabolic regions for sequences of polynomials,SIAM J. Math. Anal.,7,,,1976,344,357,,1,,

s2sj2,3,,,,,,Sakurai T.,Petkovi\'{c} M.S.,,On some simultaneous methods based on Weierstrass' correction,J. Comput. Appl. Math.,72,,,1996,275,291,,1,,

s2sj3,14,,,,,,Sakurai T.,Sugiura H.,Torii T.,Numerical factorization of a polynomial by rational Hermite interpolation,Numerical Algorithms,3,,,1992,411,418,,1,,

s2sj4,13,,,,,,Sakurai T. et al,,,A Method for Finding Cluster of Zeros of Analytic Functions,Z. Angew. Math. Mech.,76 Supp. 1,,,1996,515,516,,1,,

s2sj5,21,,,,,,Salzer H.E.,,,Equally weighted quadrature formulas over semi-infinite and infinite intervals,J. Math. and Phys.,34,,,1955,54,63,,1,,

s2sj6,21,,,,,,Salzer H.E.,,,Equally-weighted quadrature formulae for inversion integrals,Math. Tab. Aids Comput.,11,,,1957,197,200,,1,,

s2sj7,27,,,,,,Sambandham M.,,,On the real roots of random algebraic equations,Indian J. Pure Appl. Math.,7,,,1976,1062,1070,,1,,

s2sj8,27,,,,,,Sambandham M.,,,On a random algebraic equation,J. Ind. Math. Soc.,41,,,1977,83,97,,1,,

s2sj9,27,,,,,,Sambandham M.,,,On the average number of real zeros of a class of random algebraic curves,Pacific J. Math.,81,,,1979,207,215,,1,,

s2sj10,4,,,,,,San Juan R.,,,Complementos al método de Gräffe para la resolución de ecuaciones algébricas,Revista Matematica Hispano- Americano Ser. 3,1,,,1939,1,14,,1,,

s2sj11,19,20,,,,,Sansone G.,,,La risoluzione aparistica delle congruenze cubiche,Ann. Mat. Pura Appl. Ser. 4,6,,,1929,127,160,,1,,

s2sj12,19,20,,,,,Sansone G.,,,La risoluzione aparistica delle congruenze cubiche,Ann. Mat. Pura Appl. Ser. 4,7,,,1930,1,32,,1,,

s2sj13,29,,,,,,Sarakar B.P. et al,,,Economic Pseudodivision Processes for Obtaining Square-Root Logarithm and Arc Tan,IEEE Trans. Comput.,20,,,1971,1589,1593,,1,,

s2sj14,26,,,,,,Sasaki T.,,,A Study of Approximate Polynomials- I -- Representation and Arithmetic --,Japan. J. Indust. Appl. Math.,12,,,1995,137,161,,1,,

s2sj15,10,,,,,,Sasaki T.,,,Polynomial Remainder Sequences and Approximate GCD,SIGSAM Bull.,31 No. 3,,,1997,4,10,,1,,

s2sj16,10,,,,,,Sasaki T.,,,Approximate Algebraic Computation: Practise and Problems,SIGSAM Bull.,31 No. 3,,,1997,32,32,,1,,

s2sj17,11,,,,,,Saux Picart Ph. M.,,,Schur-Cohn Sub-transforms of a Polynomial,J. Symb. Comput.,16,,,1993,1,7,,1,,

s2sj18,2,4,,,,,Savenko S.,,,Iteration method for solving algebraic and transcendental equation,USSR Comp. Math. Math. Phys.,4 No. 4,,,1964,159,167,,1,,

s2sj19,19,20,,,,,Scarpis U.,,,Intorno alla Risoluzione per Radicali...,Period. Mat. Ser. 3,9,,,1912,73,79,,1,,

s2sj20,15,,,,,,Scavo T.R.,Thoo J.B.,,On the Geometry of Halley's Method,Amer. Math. Monthly,102,,,1995,417,426,,1,,

s2sj21,7,,,,,,Scheffers G.,,,über die Fehlerregel,S. Ber. Math. Ges.,15,,,1916,29,34,,1,,

s2sj22,23,,,,,,Scherberg M.G.,Riordan J.F.,,Analog calculation of polynomial and trigonometric expansions,Math. Tab. Aids Comp.,7,,,1953,61,65,,1,,

s2sj23,19,,,,,,Schlömlich,,,Neue Auflösung der biquadratischen Gleichungen,Z. Math. Phys.,6,,,1861,49,51,,1,,

s2sj24,19,,,,,,Schlömlich,,,Extrait d'une lettre addressée à M. Liouville par M. Schlömlich,J. Math. Pures Appl. Ser. 2,8,,,1863,99,100,,1,,

s2sj25,30,,,,,,Schmeisser G.,,,A real symmetric tridiagonal matrix with a given characteristic polynomial,Lin. Algebra Appl.,193,,,1993,11,18,,1,,

s2sj26,17,,,,,,Schonfelder J.L.,Razaz M.,,Error Control with Polynomial Approximations,IMA J. Numer. Anal.,1,,,1981,105,114,,1,,

s2sj27,10,,,,,,Schönhage A.,,,Probabilistic Computation of Integer Polynomial GCD's,J. Algorithms,9,,,1988,365,371,,1,,

s2sj28,23,,,,,,Schooley A.H.,,,An electro-mechanical method for solving equations,RCA Review,3,,,1938,86,96,,1,,

s2sj29,18,,,,,,Schur I.,,,On the characteristic roots of a linear substitution with an application to the theory of integral equations (German),Math. Ann.,66,,,1909,488,510,,1,,

s2sj30,19,,,,,,Schuster H.S.,,,Quadratische Gleichungen der Seleukidenzeit aus Uruk,Quellen und Studien zur Geschichte der Math.,1,,,1930,194,200,,1,,

s2sj31,29,,,,,,Schwarz E.M.,Flynn M.J.,,Hardware Starting Approximation Method and Its Application to the Square Root Operation,IEEE Trans. Comput.,45,,,1996,1356,1369,,1,,

s2sj32,20,,,,,,Schwarz S.,,,Sur le nombre des racines et des facteurs irréductibles d'une congruence donnée,Casopis Pest. Mat.,69,,,1940,128,145,,1,,

s2sj33,20,,,,,,Schwarz S.,,,On the reducibility of binomial congruences and on the bound of the least integer belonging to a given exponent mod p,Casopis Pest. Mat. Fys.,74,,,1949,1,16,,1,,

s2sj34,20,29,,,,,Scorza G.,,,La risoluzione apiristica delle congruenze binomie e la formula d'interpolazione di Lagrange,Rendiconti della R. Accademia nazionale dei Lincei,3,,,1926,390,394,,1,,

s2sj35,10,,,,,,Sederberg T.W.,Chang G.Z.,,Best linear common divisors for approximate degree reduction,Computer-Aided Design,25,,,1993,163,168,,1,,

s2sj36,20,,,,,,Segre B.,,,Arithmetische Eigenschaften von Galois-Räumen. I,Math. Ann.,154,,,1964,195,256,,1,,

s2sj37,20,,,,,,Semaev I.A.,,,Construction of irreducible polynomials over finite fields with linearly independent roots,Math. USSR Sb.,63,,,1989,507,519,,1,,

s2sj38,3,,,,,,Semerdzhiev K.,,,method for simultaneously finding all the roots of an algebraic equation given their multiplicities,(Russian) Bolgarskoi Akad. Nauk Dokl.,35,,,1982,1057,1060,,1,,

s2sj39,10,,,,,,Sendra J.R.,Llovet J.,,An Extended Polynomial GCD Algorithm Using Hankel Matrices,J. Symb. Comput.,13,,,1992,25,39,,1,,

s2sj40,27,,,,,,Shepp L.A.,Vanderbei R.J.,,The complex zeros of random polynomials,Trans. Amer. Math. Soc.,347,,,1995,4365,4384,,1,,

s2sj41,21,,,,,,Shohat J.,,,On the convergence-properties of Lagrange- interpolation etc.,Ann. of Math. Ser. II,38,,,1937,758,769,see formula 39,1,,

s2sj42,20,,,,,,Shoup V.,,,Smoothness and factoring polynomials over finite fields,Inform. Process. Lett.,38,,,1991,39,42,,1,,

s2sj43,20,,,,,,Shoup V.,,,A new polynomial factorization algorithm and its implementation,J. Symbolic Comput.,20,,,1995,363,397,,1,,

s2sj44,20,,,,,,Shparlinski I.E.,,,Finding Irreducible and Primitive Polynomials,Applicable Algebra in Engineering Comm. and Comput,4,,,1993,263,268,,1,,

s2sj45,27,,,,,,Shparo D.,Shur M.,,On the distribution of the roots of random polynomials,Vestnik Moskov. Univ. Ser. I Mat. Mekh.,3,,,1962,40,43,,1,,

s2sj46,19,,,,,,Sievens J.,,,Entwickelung der Umformung der Gleichung...,Astronomische Nachrichten,70,,,1868,353,358,,1,,

s2sj47,18,,,,,,Simeunovi\'{c} D.M.,,,Sur les zéros des polynômes de composition,Publ. Inst. Math. (Beograd),10 No. 24,,,1970,103,111,,1,,

s2sj48,29,,,,,,Sinclair R.,,,Optimization of Reciprocals and Square Roots on the i860 Microprocessor,Intern. J. High Speed Comput.,8,,,1996,57,64,,1,,

s2sj49,19,20,,,,,Skolem T.,,,The general congruence of 4th degree modulo p; p prime,Norsk. Mat. Tidsskr.,34,,,1952,73,80,,1,,

s2sj50,17,,,,,,Skrzipek M.R.,,,Polynomial evaluation and associated polynomials,Numer. Math.,79,,,1978,601,613,,1,,

s2sj51,24,10,20,,,,Slisenko A.O.,,,Complexity problems in computational theory,Russian Math. Surveys,36 No. 6,,,1981,23,125,,1,,

s2sj52,2,10,26,,,,Smale S.,,,Complexity theory and numerical analysis,Acta Numerica,6,,,1997,523,551,,1,,

s2sj53,19,,,,,,Smith D.E.,,,Unsettled Questions Concerning the Mathematics of China,Scientific Monthly,33,,,1931,244,250,,1,,

s2sj54,19,,,,,,Smith D.E.,,,Algebra of Four Thousand Years Ago,Scripta Mathematica,4,,,1936,111,125,,1,,

s2sj55,29,,,,,,Smyly J.G.,,,Square roots in Heron of Alexandria,Hermathena,63,,,1944,18,26,,1,,

s2sj56,21,,,,,,Sobolev S.L.,,,On the roots of Euler polynomials,Dokl. Akad. Nauk S.S.S.R.,18,,,1977,935,938,,1,,

s2sj57,29,,,,,,Soderquist P.,Leeser M.,,Area and Performance Trade-Offs in Floating-Point Divide and Square-Root Implementations,ACM Computing Surveys,28,,,1996,518,564,,1,,

s2sj58,21,,,,,,Sofo A.,,,Real Roots of Polynomials (Problems and Solutions),SIAM Rev.,39,,,1997,765,772,,1,,

s2sj59,19,,,,,,Spearman B.K.,Williams K.S.,,Characterization of Solvable Quintics,Amer. Math. Monthly,101,,,1994,986,992,,1,,

s2sj60,13,,,,,,Spitzer S.,,,Aufsuchung der reellen und imaginären Wurzeln einer Zahlengleichung höheren Grades,Naturwissenschaftliche Abbandlungen,3,,,1850,109,170,,1,,

s2sj61,13,,,,,,Spitzer S.,,,Bemerkungen über Herrn Jos. Popper's "Beitrage zu Weddle's Methode der Auflösung numerischer Gleichungen",Z. Math. Phys.,8,8,,,1863,240,,1,,

s2sb32,13,,,,,,Soderblom A.,,,"Résolution Numérique des équations Algébriques",,,,Goteborg,1899,,,,1,,

s2sb33,29,,,,,,Soderquist P.,Leeser M.,,An area/performance comparison of subtractive and multiplicative divide/square root implementations in "Proc. 12th Symp. on Computer Arithmetic",,,,,1995,132,139,,1,,

s2sb34,13,,,,,,Sohotzky,,,"Auflösung der numerischen Gleichungen",,,,Petersburg,1882,,,,1,,

s2sb35,13,,,,,,Spitzer S.,,,"Allgemeine Auflösung der Zahlen- Gleichungen mit einer oder mehreren Unbekannten",,,,Wien,1851,,,,1,,

s2sb36,1,7,14,,,,Stanton R.G.,,,"Numerical Methods for Science and Engineering",,,Prentice-Hall,Englewood Cliffs N.J,1961,,,,1,,

s2sb37,29,,,,,,Stearns C.C.,,,Subtractive floating-point division and square root for VLSI DSP in "European Conference on Circuit Theory and Design",,,,,1989,405,409,,1,,

s2sb38,19,,,,,,Steichen M.,,,"Memoire sur la vie et les travaux de Simon Stevin",,,,Bruxelles,1846,,,,1,,

s2sb39,2,10,19,,,,Stevenson R.,,,"Algebraic Equations",,,,Cambridge,1835,,,,1,,

s2sb40,1,2,10,14,24,,Stoer J.,,,"Einführung in die Numerische Mathematik I",,,,Berlin,1979,224,278,,1,,

s2sb41,17,,,,,,Strassen V.,,,Algebraic Complexity Theory in "Handbook of Theoretical Computer Science Algorithms and Complexity Vol. A" ed. J. van Leeuwen,,,Elsevier,Amsterdam,1990,633,672,,1,,

s2sb42,19,,,,,,Struik D.J.,,,"A Concise History of Mathematics",,,Dover,New York,1948,,,,1,,

s2sb43,19,,,,,,Sturm A.,,,"Geschichte der Mathematik",,,,Leipzig,1904,,,,1,,

s2sb44,10,,,,,,Sturm C.,,,"The Solution of Numerical Equations" Trans. J. Souter,,,,London,1835,,,,1,,

s2sb45,10,,,,,,Sturm C.,,,"Abhandlung über die Auflösung der numerischen Gleichungen" Trans. A. Loewy; Ostwald's Klassiker No. 143,,,,Leipzig,1904,,,,1,,

s2sb46,13,,,,,,Sudan M.,,,"Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems; LNCS 1001",,,Springer-Verlag,,1995,,,,1,,

s2sb47,13,,,,,,Szegö G.,,,Bemurkungen zu einem Satz von E. Schmidt über algebraische Gleichungen,Sitz. Preuss. Akad. Wiss. Phys.-Mat. Kl.,,,,1934,86,98,,1,,

s2sb48,1,2,5,7,10,14,Szidarovszky F.,Yakowitz S.,,"Principles and Procedures of Numerical Analysis",,,Plenum Pr.,New York,1978,,,,1,,

s2sb49,24,26,,,,,Szidarovszky F.,Yakowitz S.,,"Principles and Procedures of Numerical Analysis",,,Plenum Pr.,New York,1978,,,,1,,

s2sb1,2,10,19,,,,Saint-Loup L.,,,"Traité de la résolution des équations numériques",,,Mallet-Bachelier,Paris,1864,,,,1,,

s2sb2,19,,,,,,Sakabe Kohan,,,"Approximations to a root of a cubic equation (Rippo Eijiku)",,,,,1803,,,,1,,

s2sb3,10,,,,,,Salmon G.,,,"Vorlesungen über die Algebra der linearen Transformationen",,,,Leipzig,1877,,,,1,,

,11,12,0,0,0,0,Rantzer, A.,,,Stability conditions for polytopes of polynomials,IEEE Trans. Automat. Control,37 no 1,,,1992,79,89,Considers stability of families of polynomials with interval coefficients.,1,0,

,21,0,0,0,0,0,Ullman, J.L.,Wyneken, M.F.,,Weak limits of zeros of orthogonal polynomials,Constr. Approx.,2,,,1986,339,347,,1,0,

,20,0,0,0,0,0,Ullman, J.L.,Wyneken, M.F.,Ziegler, L.,Norm Oscillatory Weight Measures,J. Approx. Theory,46,,,1986,204,212,,1,0,

,11,0,0,0,0,0,Tempo, R.,,,A simple test for Schur stability of a diamond of complex polynomials, in "Proc. IEEE Conf. Dec. Control",,,,,1989,1892,1895,Considers stability of polynomials whose coefficients vary in a diamond,1,0,

,21,0,0,0,0,0,Elbert, A.,Laforgia, A.,,Asymptotic formulas for ultraspherical polynomials P_n^(λ)(x) and their zeros, for large values of λ,Proc. Amer. Math. Soc.,114,,,1992,371,377,,1,0,

,25,0,0,0,0,0,Bourgne, R.,Azra, J.-P. (Eds),,Ecrits et mémoires mathématiques d'Évariste Galois,,,Gauthier-Villars,Paris,1962,0,0,Considers solubility by radicals,1,0,

,25,0,0,0,0,0,Dahan, A,,,Les travaux de Cauchy sur les substitutions. Etude de son approche du concept de groupe,Arch. Hist. Exact Sci.,23,,,1980,279,319,Considers solubility by radicals,1,0,

,25,0,0,0,0,0,Liouville, J. (Ed.),,,Oeuvres mathématiques d'Évariste Galois,J. Math. Pures Appl.,11,,,1846,381,444,Solution by radicals,1,0,

,25,0,0,0,0,0,Taton, R.,,,Les relations d'Evariste Galois avec les mathématiciens de son temps,Revue hist. Sci.,1,,,1947,114,130,,1,0,

,25,0,0,0,0,0,Taton, R.,,,Galois, Évariste,Dict. Sci. Biog.,5,,,1972,259,265,Summary of Galois' life and work, including solubility by radicals.,1,0,

,18,21,0,0,0,0,Ismail, M.E.H.,Li, X.,,Bounds on the extreme zeros of orthogonal polynomials,Proc. Amer. Math. Soc.,115,,,1992,131,141,,1,0,

,10,21,0,0,0,0,Marden, M.,,,A rule of signs involving certain orthogonal polynomials,Ann. Math. Ser. 2,33,,,1932,118,124,A Sturm-like theorem,1,0,

,13,0,0,0,0,0,Wylie, A.,,,Chinese Researches,,,,Taipei,1966,170,174,,1,0,

,20,0,0,0,0,0,Cahen, E.,,,Théorie des nombres,,,Gauthier-Villars et Cie.,Paris,1914,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Gunji H.,Arnon D.,,On polynomial factorization over finite fields.,Math. Comp.,36,,,1981,281,287,Finds degrees of factors.,1,0,

,20,0,0,0,0,0,Gao S.,,,On the deterministic complexity of factoring polynomials.,J. Symb. Comput.,31,,,1999,19,36,Can factor in polynomial time in nearly all cases.,1,0,

,21,0,0,0,0,0,Driver K.,Duren P.,,Zeros of the hypergeometric polynomials. F(-n,b;2b;z),Indag. Math.,11,,,2000,43,51,Considers also Jacobi polynomials.,1,0,

,25,0,0,0,0,0,Novy, L.,,,Origins of Modern Algebra, trans J. Tauer,,,Academia,Prague,1973,0,0,Treats existence,1,0,

,10,0,0,0,0,0,Speziali, P.,,,F. Sturm,Dict. Sci. Biog.,13,,New York,1976,126,132,Brief statement of Sturm's theorem,1,0,

,17,0,0,0,0,0,Hellerman, H.,,,Parallel processing of algebraic expressions,IEEE Trans. Comput.,15,,,1966,82,91,Includes evaluation of polynomials,1,0,

,1,0,0,0,0,0,Shedler, G.S.,,,Parallel numerical methods for solutions of equations,Comm. A.C.M.,10,,,1967,286,290,Generalization of Bisection Method,1,0,

,25,0,0,0,0,0,Dickson, L.E.,,,Algebraic Theories,,,Dover,New York,1959,0,0,Solution by radicals,1,0,

,3,0,0,0,0,0,Iliev, A.I.,Semerdzkiev, K.I.,,On a Generalization of the Obreshkoff-Ehrlich method for simultaneous extraction of all roots of polynomials over an arbitrary Chebyshev system.,Comput. Math. Math. Phys.,41,,,2001,1385,1392,,1,0,

,19,29,0,0,0,0,Rashed, R.,,,"The Development of Arabic Mathematics: between Arithmetic and Algebra", trans A.F.W. Armstrong,,,,Paris,1994,,,Arabic treatment of roots and low-degree equations,1,0,

,19,0,0,0,0,0,kowol,,,Science Awakening,,,Basel-Stuttgart,,1956,0,0,Brief treatment of quadratics by Babylonians,1,0,

,15,0,0,0,0,0,Hernandez, M.,,,Newton-Raphson's Method and Convexity,Zb. Radova Prirod.-Mat. Fak. Ser. Mat.,22,,,1993,159,166,Derives a method involving f''(x)/[f'(x)]²,1,0,

,21,0,0,0,0,0,Kokologiannaki, C.G.,Siafarikas, P.D.,,Convexity of the largest zero of the ultraspherical polynomials,Integral Trans. Special Functions,4,,,1996,1,6,,1,0,

,17,0,0,0,0,0,Hyafil, L.,Kung. H.T.,,The complexity of parallel evaluation of linear recurrences,J. Assoc. Comput. Mach.,24,,,1977,513,521,If b_i=x (all i) this is equivalent to Homer's method.,1,0,

,17,0,0,0,0,0,Kowalik, J.S.,Kumar, S.P.,,Parallel algorithms for recurrence and tridiagonal equations, in "Parallel MIMD Computation:HEP Supercomputer and its Applications", ed. J.S. Kowalik,,,MIT Press,,1985,295,307,If b_i=x (all i) this is equivalent to Homer's method.,1,0,

,2,4,5,6,10,0,John, F.,,,Lectures on Advanced Numerical Analysis,,,Nelson,,1966,0,0,Covers methods of Sturm, Bernouilli, Graeffe, Lehmer, Newton,1,0,

,21,0,0,0,0,0,Driver K.,Duren P.,,Trajectories of the zeros of hypergeometric polynomials F(-n;b;2b;z) for b < 1/2,Constr. Approx.,17,,,2001,169,179,no note.,1,0,

,15,0,0,0,0,0,Gerlach J.,,,Accelerated convergence in Newton's method.,SIAM Rev.,36,,,1994,272,276,Generalizes Halley's method. Probably not practicable.,1,0,

,21,0,0,0,0,0,Meijer M.G.,de Bruin M.G.,,Zeros of Sobolev orthogonal polynomials following from coherent pairs.,J. Comput. Appl. Math.,139,,,2002,253,274,Considers position of zeros with respect to those of Languerre & Jacobi polynomials.,1,0,

,19,0,0,0,0,0,Winter H.J.J.,Arafat W.,,The Algebra of 'Umar Khayyam',J. Roy. Asiatic. Soc. Bengal,16,,,1950,27,77,Early treatment of quadratic and special cubics.,1,0,

,1,2,7,,0,0,Phillips, G.M.,Taylor, P.J.,,Theory and Applications of Numerical Analysis,,,Academic Press, Inc.,New York,1974,0,0,Treats Bisection, reguli falsi, Muller, Newton,1,0,

,1,2,7,16,0,0,Rheinboldt, W.C.,,,Algorithms for Finding Zeros of Functions,UMAP Journal,2,,,1981,43,72,Considers bisection, secant, Newton, roundoff, convergence.,1,0,

,1,2,7,14,0,0,Shoup T.E.,,,A Practical Guide to Computer Methods for Engineers,,,Prentice-Hall, Inc.,Englewood, N.J.,1979,0,0,Treats bisection, Newton, secant and Bairstow.,1,0,

,1,2,7,14,0,0,Shoup, T.E.,,,Numerical Methods for the Personal Computer,,,Prentice-Hall, Inc,Englewood, N.J.,1983,0,0,Treats bisection, Newton, secant and Bairstow.,1,0,

,1,2,7,14,17,0,Smith, W.A.,,,Elementary Numerical Analysis,,,Prentice-Hall, Inc.,Englewood, N.J.,1986,0,0,Treats bisection, Newton, secant, Bairstow, and evaluation.,1,0,

,1,2,7,0,0,0,Maron, M.J.,,Lopez,Numerical Analysis: A Practical Approach,,,Wadsworth Publishing Co.,California,1991,0,0,Treats bisection, Newton, secant.,1,0,

,1,7,0,0,0,0,Miller, W.,,,The Engineering of Numerical Software,,,Prentice-Hall , Inc.,Englewood, N.J.,1984,0,0,Treats bisection, secant, and combination of them.,1,0,

,2,7,14,0,0,0,Milne. W.E.,,,Numerical Calculus,,,Princeton Univ. Press,Princeton, N.J.,1949,0,0,Treats variation on Newton, secant and also Bairstow.,1,0,

,2,26,0,0,0,0,Moursund, D.G.,Duris, C.S.,,Elementary Theory and Application of Numerical Analysis,,,McGraw-Hill Book Co.,New York,1967,0,0,Treats Newton method, errors.,1,0,

,19,0,0,0,0,0,Dedron, P.,Itard, J.,,Mathématiques et mathématiciens,,,Magnard,Paris,1959,0,0,Geometric (Greek) treatment of quadratics.,1,0,

,1,2,7,10,,,Borse, G.J.,,,Fortran77 and Numerical Methods for Engineers,,,Prindle, Weber & Schmidt,Boston,1985,0,0,Treats bisection, Newton, secant, Descartes' rule,1,0,

,2,6,10,14,16,24,Blum, E.K.,,,Numerical Analysis and Computation: Theory and Practise,,,Addison-Wesley Publ. Co,,Reading, Mass,1972,0,0,Treats Newton, Bernoulli, Bairstow, Sturm, convergence, acceleration.,1,0,

,19,0,0,0,0,0,Kasir D.S.,,,The Algebra of Omar Khayyam,,,J.J. Little and Ives Co.,New York,1931,0,0,Arabic treatment of quadratic and cubic.,1,0,

,11,0,0,0,0,0,Garloff, J.,Bose, N.K.,,Boundary implications for stability properties: present status, in "Reliability in Computing: The Role of Interval Methods in Scientific Computing",,,Academic Press,San Diego,1988,391,402,,1,0,

,2,6,16,17,0,0,Stiefel, E.,,,Einführung in die numerische mathematik,,,Teubner,Stuttgart,1963,0,0,Fairly good treatment of Newton, Bernoulli, convergence, evaluation.,1,0,

,13,0,0,0,0,0,Fogiel, M.,,,Numerical Analysis Problem Solver,,,REA,New York,1983,0,0,Gives examples of many methods, but hardly explains them.,1,0,

,2,19,29,0,0,0,Lacroix, S.F.,,,Élémens d'Algèbre,,,Bachelier,Paris,1847,0,0,Treats Newton, quadratic, and surds.,1,0,

,11,0,0,0,0,0,Kharitonov B.L.,,,The Routh-Hurwitz problem for families of polynomials and quasi-polynomials.,Mat. Fiz.,26,,,1979,69,79,Including pg. 128.,1,0,

,13,0,0,0,0,0,Ruffini P.,,,Beweis der unmoglichkeit vollstandie alg. Gleichungen…,Z. Math. Phys.,1,,,1826,253,262,No note.,1,0,

,19,0,0,0,0,0,Karpinski L. Ch.,,,The Italian Arithmetic and Algebra of Jacob of Florence.,Archeion,11,,,1929,170,177,Mentions early Medieval treatment of quadratic.,1,0,

,1,2,7,14,17,24,Atkinson L.V.,Harley P.J.,,Introduction to Numerical Methods with Pascal.,,,Addison-Wesley,,1983,0,0,Treats Bisection, Newton, Secant, Bairstow, Evaluation, and Acceleration.,1,0,

,19,0,0,0,0,0,Eves H.,,,Omar Khayyam's Solution of Cubic Equations,Math. Teacher,51,,,1958,285,286,Geometrical method with circle and hyperbola.,1,0,

,1,2,7,16,0,0,Dew P.M.,James K.R.,,Introduction to Numerical Computation in Pascal.,,,Springer-Verlag,New York,1983,0,0,Treats Bisection, Newton, Secant, and Hybrid; Convergence.,1,0,

,2,10,0,0,0,0,Dodes I.A.,,,Numerical Analysis for Computer Science.,,,North-Holland,New York,1978,0,0,Treats Newton, Sturm.,1,0,

,1,2,7,14,15,16,Gerald C.F.,Wheatley P.O.,,Applied Numerical Analysis 6th ed.,,,Addison-Wesley,Reading, Mass.,1999,0,0,Treats Bisection, Newton, Secant, Muller, Bairstow, QD, Graffe, Lehmer, Laguene, and convergence.,1,0,

,19,0,0,0,0,0,Frink O. Jr.,,,A method for solving the cubic.,Amer. Math. Monthly,32,,,1925,134,134,Fairly simple method.,1,0,

,19,0,0,0,0,0,Kalman D.,White J.,,A simple solution of the cubic,College Math. J,29,,,1998,415,418,Allegedly simple solution of the cubic- takes 3 pages.,1,0,

,19,29,10,25,0,0,Katz V.J.,,,A History of Mathematics- an Introduction,,,Harper Collins,New York,1993,0,0,Treats square roots, quadratic, cubic, existence, Descartes rule.,1,0,

,19,0,0,0,0,0,Oglesby E.J.,,,Note on the algebraic solution of the cubic,Amer. Math. Monthy,30,,,1923,321,323,Gives Cardan's solution by a different method.,1,0,

,19,0,0,0,0,0,Pen-Tung Sah, A.,,,A uniform method of solving cubics and quartics.,Amer. Math. Monthy,52,,,1945,202,206,Uses determinants.,1,0,

,19,0,0,0,0,0,Suen R.Y.,,,Roots of cubics via determinants.,College Math. J.,25,,,1994,115,117,Uses an auxillary quadratic and determinants to give "easily remembered" solution of cubic.,1,0,

,19,0,0,0,0,0,White C.R.,,,Definitive solutions of general quartic and cubic equations.,Amer. Math. Monthy,69,,,1962,285,287,No note.,1,0,

,19,0,0,0,0,0,White J.E.,,,Cubic Equations (a Mathwright workbook) on web-page www.mathwright.com/book_pgs/book241.html,The New Mathwright Library (web pg.),,,,0,0,0,Explains Cardan's solution and generalizes to higher order.,1,0,

,19,25,0,0,0,0,Calinger R. (ed),,,Classics of Mathematics,,,Moore Publishing,Oak Park Illinios,1982,0,0,Original papers on low-degree polynomials and existence.,1,0,

,21,0,0,0,0,0,van Doorn, E.A.,,,On a class of generalized orthogonal polynomials with real zeros, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,231,236,,1,0,

,21,0,0,0,0,,Förster, K.-J.,Petras, K.,,On the zeros of ultraspherical polynomials and Bessel functions, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,257,262,,1,0,

,21,0,0,0,0,0,Gori, l.,Lo Cascio, M.L.,,On an invariance property of the zeros of some s-orthogonal polynomials, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,277,280,,1,0,

,19,0,0,0,0,0,Vogel, K.,,,Leonardo of Pisa, in "Dictionary of Scientific Biography", Vol. 4,,,,New York,1971,604,613,Gives geometric problems leading to quadratics,1,0,

,11,0,0,0,0,0,Bose, N.K.,Shi, Y.Q.,,Network realizability approach to stability of complex polynomials,IEEE Trans. Circuits Systems,34,,,1987,216,218,,1,0,

,25,,0,0,0,0,Malfatti,,,Dubbj Proposti al Socio Paolo Ruffini Sulla Sua Dimostrazione Della Impossibilita di Risolvere le Equazioni Superiori al Quarto Grado,Mem. Mat. Fiz. Ser. Ital. Sci.,11,,,1804,579,607,Considers solution by radicals for degree > 4,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Riflessioni Intorno al Metodo Proposta dal Consocio Malfatti per la Soluzione Delle Equazioni di 5 Grado,Mem. Mat. Fiz. Soc. Ital. Sci.,12,,,1805,321,336,Considers solution by radicals for degree > 4,1,0,

,25,0,0,0,0,0,Ruffini,,,Riposta di Paolo Ruffini al Dubbj Propostigli dal Socio Gian-Francesco Malfatti Sopra la Insolubilita' Algebraica Dell' Equazioni di Grado Superiore al Quarto.,Mem. Mat. Fiz. Soc. Ital. Sci.,11,,,1804,213,267,No note.,1,0,

,2,15,19,0,0,0,Stroud K.A.,,,Further Engineering Mathematics,,,MacMillan,London,1986,0,0,Treats cubic, quartic, Newton's method, and one involving second derivative.,1,0,

,19,0,0,0,0,0,Munem M.A.,Foulis D.J.,,Algebra and Trigonometry with Applications,,,Worth Publ.,New York,1982,0,0,Treats quadratic.,1,0,

,25,0,0,0,0,0,Abel N.H.,Galois E.,,Abhandlungen über die algebraische Auflösung der Gleichungen.,,,Springer,Berlin,1889,0,0,Treats solubility by radicals.,1,0,

,2,24,0,0,0,0,Nitsche J.,,,Praktische Mathematik,,,Bibl. Inst.,Mannheim,1968,0,0,Covers Newton, and acceleration.,1,0,

,2,14,24,26,0,0,Noble B.,,,Numerical Methods 1,,,Oliver & Boyd,Edinburgh,1964,0,0,Covers Newton & Bairstow methods, acceleration and errors.,1,0,

,19,29,0,0,0,0,Gunther S.,,,Geschichte der Mathematik 1,,,,Leipzig,1908,0,0,Early treatment of surds; cubic and quartic solution.,1,0,

,19,0,0,0,0,0,Vygodsky M.,,,Mathematical Handbook: Elementary Mathematics,,,Mir Publ.,Moscow,1979,0,0,Treats quadratic.,1,0,

,3,15,0,0,0,0,Petkovic M.S.,Vranic D.V.,,The Convergance of Euler-like Method for the Simultaneous Inclusion of Polynomial Zeros.,Comput. Math. Appl.,39 (8),,,2000,95,105,Uses circular arithmetic; gives fourth order convergence & safe initial conditions.,1,0,

,2,4,7,16,17,18,Werner H.,,,Praktische Mathematik 1,,,Springer,Berlin,1970,0,0,Covers Newton, Secant, Convergence, Muller, Evaluation, Graeffe, Fourier-Budan and Bounds.,1,0,

,2,6,7,14,24,0,Morris J.L.,,,Computational Methods in Elementary Numerical Analysis,,,Wiley,New York,1983,0,0,Treats Newton, QD, Secant, Bairstow, and Acceleration.,1,0,

,19,0,0,0,0,0,Enriques F.,,,La Matematiche Nella Storia e Nella Cultura.,,,Zanichelli,Bologna,1938,0,0,Brief treatment of cubic.,1,0,

,3,12,16,0,0,0,Petkovic M.S.,Trajcovic M.,,On the R-order of convergence of dependent sequences involved in iterative processes, in "Proc. VIII Conf. Appl. Math." ed. Jacimovic,,,,,1993,197,206,Analyses R-order of convergence of dependant sequences, including interval methods.,1,0,

,2,4,0,0,0,0,McNeary S.S.,,,Introduction to Computational Methods for Students of Calculus.,,,Prentice-Hall,,1973,0,0,Elementary treatment of Newton and Graeffe's methods.,1,0,

,1,2,7,0,0,0,Pizer S.M.,Wallace V.L.,,To Compute Numerically,,,Little, Brown & Co.,Boston,1983,0,0,Treats Bisection, Newton, Secant, and Hybrid methods. Good treatment of errors.,1,0,

,0,0,0,0,0,0,Bini D.,Pan V.,,Parallel Polynomial Computations by Recursive Processes, in "ISSAC '90",,,ACM Press,New York,1990,294,0,No note.,1,0,

,19,29,0,0,0,0,Becker O.,Hoffmann J.E.,,Geschichte der Mathematik,,,Athenaum-Verlag,Bonn.,1951,0,0,Brief treatment of surds & low degree polynomials.,1,0,

,10,0,0,0,0,0,Sturm, C.,,,Sur la résolution des équations numériques,Bulletin de Férussac,12,,,1829,318,0,No note.,1,0,

,10,20,0,0,0,0,Wang P.,,,Parallel Polynomial Operations: a progress report, in "Proc. PASCO '94", ed Hong H.,,,RISC,Linz,1994,394,404,Considers parallel factorization mod primes, and GCD's.,1,0,

,10,0,0,0,0,0,Collins G.E. et al,,,Parallel Real Root Isolation Using the Coefficient Sign Variation Method, in "Computer Algebra and Parallelism" ed Zippel R.,Proc. Second Intern. Workshop,,Springer-Verlag,,1990,71,87,Uses Descartes rule of signs and bisection.,1,0,

,3,0,0,0,0,0,Iliev, A,,,A Generalization of Obreshkoff-Erlich Method for roots of Polynomial Equations,C.R.Acad Bulgare Sci.Math.Nat.,49,,,1996,23,26,Useful if multiplicities known,1,0,

,19,0,0,0,0,0,Notari, V.,,,Equzione de Quarto Grado,Perio. Mat.,4,,,1924,327,334,Historical treatment of quartic.,1,0,

,19,0,0,0,0,0,Karpinski,,,The origin and development of algebra,School Sci. Math.,23,,,1923,54,64,Early treatment of quadratic,1,0,

,19,29,0,0,0,0,Dedron, P.,Itard, J.,,Mathématiques et mathématiciens,,,Open Univ. Press,,1973,0,0,Roots and quadratics,1,0,

,2,19,0,0,0,0,Pearson, Carl E. (ed),,,Handbook of Applied Mathematics,,,Van Nostrand Rhinehold,New York,1983,0,0,Treats low-degree and Newton,1,0,

,2,19,0,0,0,0,Stephenson, G.,,,Mathematical methods for Science Students,,,Longman,London,1973,0,0,Treats cubic and Newton's method,1,0,

s2rj19,18,,,,,,Riddell R.C.,,,Location of the zeros of a polynomial relative to a certain disk,Trans. Amer. Math. Soc.,205,,,1975,37,45,,1,,

s2rj20,13,,,,,,Risler J.-J.,Ronga F.,,Testing Polynomials,J. Symb. Comput.,10 No. 1,,,1990,1,5,,1,,

s2rj21,16,,,,,,Ritter K.,,,Average errors for zero finding: lower bounds for smooth or monotone functions,Aequationes Math.,48,,,1994,194,219,,1,,

s2rj22,16,,,,,,Ritter K.,,,Some Average Case Results for Nonlinear Numerical problems,Z. Angew. Math. Mech.,76 Supp. 3,,,1996,120,123,,1,,

s2rj23,19,,,,,,Roberts M.,,,Note sur les équations du quatrième degré,Nouv. Ann. Math.,18,,,1859,87,89,,1,,

s2rj24,21,,,,,,Ronveaux A.,Zarbo A.,Godoy E.,Fourth-order differential equations satisfied by the generalized co-recursive of all classical orthogonal polynomials. A study of their distribution of zeros.,J. Comput. Appl. Math.,59,,,1995,295,328,,1,,

s2rj25,20,,,,,,Rónyai L.,,,Factoring polynomials modulo special primes,Combinatorica,9,,,1989,199,206,,1,,

s2rj26,20,,,,,,Rónyai L.,,,Galois groups and factoring polynomials over finite fields,SIAM J. Discrete Math.,5,,,1992,345,365,,1,,

s2rj27,25,,,,,,Rosen M.I.,,,Niels Hendrik Abel and Equations of the Fifth Degree,Amer. Math. Monthly,102,,,1995,495,505,,1,,

s2rj28,31,,,,,,Rossi C.,,,Sopra la risoluzione generale per serie delle equazioni algebriche,Giorn. Mat.,44,,,1906,279,290,,1,,

s2rj29,20,,,,,,Rothschild L.P.,Weinberger P.J.,,Factoring polynomials over algebraic number fields,ACM Trans. Math. Software,2,,,1977,335,350,,1,,

s2rj30,20,,,,,,Rothstein M.,Zassenhaus H.,,Deterministic analysis of aleatoric methods of polynomial factorization over finite fields,J. Number Theory,47,,,1994,20,42,,1,,

s2rj31,18,,,,,,Rubinstein Z.,Melas A.D.,,Polynomials With No Zeros in a Disk,Amer. Math. Monthly,103,,,1996,177,181,,1,,

s2rj32,19,,,,,,Runge C.,,,über die auflösbaren Gleichungen von der form x⁵+ux+ν=0,Acta Math.,7,,,1886,173,186,,1,,

s2rj33,19,,,,,,Rutherford W.,,,New and Simple Process for Determining the Three Roots of a Cubic Equation,The Mathematician,2,,,1850,257,259,,1,,

s2rb1,2,7,15,16,,,Rabinowitz P.,,,"Numerical Methods for Nonlinear Equations",,,Gordon and Breach,London,1970,,,,1,,

s2rb2,2,19,29,,,,Rashed R.,,,"The Developement of Arabic Mathematics: Between Arithmetic and Algebra",,,Kluwer,Dordrecht,1994,,,,1,,

s2rb3,19,,,,,,Rashed R.,Ahmad S.,,"Al-bakir en Algèbre d'As-Samawal",,,University of Damascus,,1972,,,,1,,

s2rb4,19,,,,,,Rashed R.,Djebbar A. eds,,"L'Oeuvre algèbrique d'al-Khayyam",,,,Paris,1980,,,,1,,

s2rb5,28,,,,,,Rassias M. Th.,,,On certain properties of polynomials and their derivative in "Topics in Mathematical Analysis" ed. Th. M. Rassias,,,World Scientific,,1989,758,802,,1,,

s2sj62,13,,,,,,Stern,,,Remarques sur une théorème énoncé par M. Fourier,J. Reine. Angew. Math.,9,,,1832,305,311,,1,,

s2sj63,9,30,,,,,Stewart G.W.,,,On the convergence of Sebastiao e Silva's method for finding a zero of a polynomial,SIAM Rev.,12,,,1970,458,460,,1,,

s2sj64,8,,,,,,Stolan J.A.,,,An improved \v{S}iljak's algorithm for solving polynomial equations converges quadratically to multiple roots,J. Comput. Appl. Math.,64,,,1995,247,268,,1,,

s2sj65,28,,,,,,Storozhenko E.A.,,,A problem of Mahler on the zeros of a polynomial and its derivative,Mat. Sb.,187,,,1996,735,744,,1,,

s2sj66,17,,,,,,Stoss J.,,,The complexity of evaluating interpolation polynomials,Theoret. Comput. Sci.,41,,,1985,319,323,,1,,

s2sj67,19,,,,,,Strehlke F.,,,Bemerkung zu der Eulerschen Auflösungsmethode der biquadratischen Gleichungen,J. Reine. Angew. Math,12,,,1834,358,359,,1,,

s2sj68,3,30,,,,,Strobach P.,,,The Recursive Companion Matrix Root Tracker,IEEE Trans. Signal Processing,45,,,1997,1931,1942,,1,,

s2sj69,10,,,,,,Sturm C.,,,Théoreme sur les racines imaginaires,Nouv. Ann. Math.,5,,,1846,115,116,,1,,

s2sj70,11,,,,,,Sun C.K.,\v{S}iljak D.D.,,Absolute Stability Test for Discrete Systems,Electronics Letters,5,,,1969,236,236,,1,,

s2sj71,29,,,,,,Suter H.,,,über das Rechenbuch des... el-Nasawî,Bibliotheca Mathematica (Stockholm) Ser. 3,7,,,1906,113,119,,1,,

s2sj72,19,,,,,,Sylvester J.J.,,,On the so-called Tschirnhausen Transformation,J. Reine Angew. Math.,100,,,1887,465,465,,1,,

s2sj73,18,,,,,,Szapiel M.,,,On annuli containing the zeros of polynomials,Demonstratio Math.,22,,,1989,755,762,,1,,

s2sj74,28,,,,,,Sz.-Nagy G.,,,Ueber geometrische Relationen zwischen den Wurzeln einer Algebraischen Gleichung und ihrer Derivierten,Jahresber. Deutsch. Math.-Verein.,27,,,1918,44,48,,1,,

s2sb25,2,,,,,,Simpson T.,,,"Essays.... on Mathematics",,,,London,1740,81,81,,1,,

s2sb26,19,29,31,,,,Simpson T.,,,"A Treatise of Algebra",,,,London,1745,,,see also Microfiche Readex c. 1970,1,,

s2sb27,20,,,,,,Sims C.C.,,,The Role of algorithms in the teaching of algebra in "Topics in Algebra" M.F. Newman ed.,,,Springer-Verlag,,1978,95,107,,1,,

s2sb28,17,,,,,,Sinclair R.,,,Tight Floating Point Error Bounds for Polynomial Evaluation in "Numerical Methods and Error Bounds" ed G.Alefeld and J. Herzberger,,,Akademie Verlag,,1996,234,240,,1,,

s2sb29,10,,,,,,Smedley T.J.,,,A new modular algorithm for computation of algebraic number polynomial gcds in "Proc. ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation",,,ACM Press,,1989,91,94,,1,,

s2sb30,13,,,,,,Smith D.E.,Mikami Y.,,"A History of Japanese Mathematics",,,,Chicago,1914,,,,1,,

s2sb31,20,29,,,,,Smith H.J.S.,,,"Collected Mathematical Papers Vol. 1",,,Chelsea Publ. Co.,New York,1965,93,162,,1,,

s2sb4,19,25,,,,,Sanford V.,,,"A short History of Mathematics",,,,Boston,1930,,,,1,,

s2sb5,19,,,,,,Sato,,,"Kongenki",,,,,1666,,,,1,,

s2sb6,19,,,,,,Sayili A.,,,"The Algebra of Ibn Turk",,,,Ankara,1962,,,,1,,

s2sb7,7,13,,,,,Scheffler H.,,,"Die Auflösung der algebraischen und transzendenten Gleichungen...",,,,Braunschweig,1859,,,,1,,

s2sb8,2,6,10,,,,Scheid F.,,,"Numerical Analysis; Schaum's Outline Series",,,McGraw-Hill,New York,1988,,,,1,,

s2sb9,2,4,7,,,,Schönhage A.,,,"The Fundamental Theorem of Algebra in Terms of Computational Complexity",,,Dept. of Mathematics,Univ. of Tubingen,1982,,,,1,,

s2sb10,13,,,,,,Schonhage S.,,,Factorization of univariate polynomials by diophantine approximation and an improved basis reduction algorithm in "Proc. ICALP '84; LNCS 172",,,,,1984,436,447,,1,,

s2sb11,25,,,,,,Schreier O.,Sperner E.,,"Introduction to Modern Algebra and Matrix Theory 2/E",,,Chelsea,New York,1959,,,,1,,

s2sb12,2,7,10,17,19,25,Schrutka L.,,,"Elemente der höheren Mathematik",,,F. Deutike,Leipzig,1921,,,,1,,

s2sb13,29,,,,,,Schwarz E.M.,Flynn M.J.,,Hardware Starting Approximation for the Square Root Operation in "Proc. 11th Symp. Computer Arithmetic",,,,,1993,103,111,,1,,

s2sb14,17,,,,,,Scott N.R.,,,"Computer Number Systems and Arithmetic",,,Prentice-Hall,Englewood Cliffs NJ,1985,235,242,,1,,

s2sb15,19,,,,,,Seki,,,"Kaiho Hompen (Various topics about equations)",,,,,1700,,,,1,,

s2sb16,3,4,5,6,15,18,Sendov Bl.,Andreev A.,Kjurkchiev N.,Numerical Solution of Polynomial Equations in "Handbook of Numerical Analysis Vol. 3" eds. P.G. Ciarlet and J.L. Lions,,,Noth-Holland,Amsterdam,1994,625,776,,1,,

s2sb17,1,2,14,,,,Shammas N.C.,,,"C/C++ Mathematical Algorithms for Scientists and Engineers",,,McGraw-Hill,New York,1995,,,,1,,

s2sb18,20,29,,,,,Shanks D.,,,Five number theoretic algorithms in "Proc. Second Manitoba Conf. on Numerical Math.",,,,,1972,51,70,,1,,

s2sb19,20,,,,,,Shoup V.,,,Fast Construction of Irreducible Polynomials over Finite Fields in "Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms",,,ACM Press,New York,1993,484,492,see also J. Symb. Comput. Vol 17 1994 pp 371-392,1,,

s2sb21,17,,,,,,Shoup V.,Smolensky R.,,Lower Bounds for Polynomial Evaluation and Interpolation Problems in "Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science",,,IEEE Computer Science Pre,,1991,378,383,,1,,

s2sb22,19,,,,,,Shurman J.,,,"Geometry of the Quintic",,,Wiley,New York,1997,,,,1,,

s2sb23,18,,,,,,\v{S}iljak D.D.,,,Algebraic criteria for positive realness relative to the unit circle in "Proc. Second International Symposium on Network Theory",,,,Herceg- Novi Yugosla,1972,151,158,,1,,

s2tj1,29,,,,,,Takagi N.,Yajima S.,,A square root hardware algorithm using redundant binary representation,Systems and Computers in Japan,17 No. 11,,,1986,30,41,,1,,

s2tj2,13,,,,,,Talbot H.F.,,,Essay toward a General Solution of Numerical Equations of all Degrees having Integer Roots,Trans. Roy. Soc. Edinburgh,27,,,1875,303,312,,1,,

s2tj3,20,29,,,,,Tamarkine J.,Friedmann A.,,Sur les congruences du second degré et les nombres de Bernoulli,Math. Ann.,62,,,1906,409,412,,1,,

s2tj4,19,,,,,,Tannery P.,,,Memoires Scientifiques Vol. 1,,,Gauthier-Villars,Paris,1876,254,280,,1,,

s2tj5,18,,,,,,Tchebicheff,,,Questions,Nouv. Ann. Math.,15,,,1856,387,387,see also ibid Ser. 2 Vol. 17 (1878) 331; ibid Ser. 2 Vol. 19 (1880) 95,1,,

s2tj6,21,,,,,,Tchebyshev P.L.,,,Sur les quadratures,J. Math. Pures Appl. Ser. 2,19,,,1874,19,34,also Oeuvres Vol. 2 Chelsea New York 165-180,1,,

s2tj7,19,,,,,,Terquem,,,équation du quatrième degré,Nouv. Ann. Math.,19,,,1860,14,17,,1,,

s2tj8,19,,,,,,Terquem,,,Résolution trigonométrique d'une équation du troisième degré,Nouv. Ann. Math.,20,,,1861,421,421,,1,,

s2tj9,13,18,,,,,Thibault,,,Sur la recherche des limites des racines d'une équation; et sur la determination des racines commensurables,Nouv. Ann. Math.,2,,,1843,517,527,,1,,

s2tj11,2,,,,,,Thomas D.J.,,,Joseph Raphson F.R.S.,Notes and Records Roy. Soc. London,44,,,1990,151,167,,1,,

s2tj12,20,,,,,,Thouvenot S.,Châtelet F.,,Au sujet des congruences de degré supérieur a deux,L'Enseignement Math. Ser 2,13,,,1967,89,98,,1,,

s2tj13,32,,,,,,Tilli P.,,,Polynomial Root Finding by Means of Continuation,Computing,59,,,1997,307,324,,1,,

s2tj14,2,15,,,,,Timmermans A.,,,Sur la résolution des équations numériques,Correspondance Mathematique et Physique,2,,,1826,218,221,,1,,

s2tj15,26,30,,,,,Toh K.-C.,Trefethen L.N.,,Pseudozeros of polynomials and pseudospectra of companion matrices,Numer. Math.,68,,,1994,403,425,,1,,

s2tj16,18,,,,,,Tomi\'{c} M.,,,Généralisation et démonstration géométrique de certains théorèmes de Fejér et Kakeya,Acad. Serbe. Sci. Publ. Inst. Math.,2,,,1948,146,156,,1,,

s2tj17,18,,,,,,Tonkov T.T.,,,Estimate of the moduli of the roots of a polynomial,USSR Comp. Math. Math. Phys.,4 No. 4,,,1964,174,175,,1,,

s2tj18,10,,,,,,Torii T. et al,,,A Stably Modified Euclidean Algorithm for Complex Coefficient Polynomials,Z. Angew. Math. Mech.,76 Supp. 1,,,1996,565,566,,1,,

s2tj19,19,,,,,,Tortolini B.,,,Sulla Risoluzione algebrica dell'equazioni di terzo e quarto grado,Ann. Mat. Pura Appl. Ser. 1,1,,,1858,310,322,,1,,

s2tj20,19,,,,,,Tortolini B.,,,Risoluzione di un problema relativo all'equazioni di terzo grado,Ann. Mat. Pura Appl. Ser. 1,7,,,1865,297,800,,1,,

s2tj21,18,,,,,,Toussaint,,,Sur la Limite des Racines,Nouv. Ann. Math. Ser. 2,18,,,1879,310,313,,1,,

s2tj22,29,,,,,,Treutlein P.,,,Das Rechnen im 16 Jahrhundert,Z. Math. Phys.,22 Supp.,,,1877,,,,1,,

s2tj23,19,,,,,,Treutlein P.,,,Die deutsche Coss,Z. Math. Phys.,24 Supp. 1,,,1879,,,,1,,

s2tj24,20,,,,,,Trotter H.F.,,,Statistics on factoring polynomials mod p and p-adically,ACM SIGSAM,16 No. 3,,,1982,24,29,,1,,

s2tj25,4,,,,,,Turan P.,,,On approximative solution of algebraic equation,Publ. Math. Debrecen,2,,,1951,26,42,,1,,

s2tj26,4,5,,,,,Turan P.,,,On the Solution of Algebraic Equations,Magyar Tud. Akad. Budapest Mat. Fiz. Tud.,18,,,1968,223,235,,1,,

s2tb1,2,19,,,,,Tannery J.,,,"Notions de Mathématiques",,,,Paris,1902,324,348,,1,,

s2tb2,19,,,,,,Tartaglia,,,"Inventioni",,,,,1546,,,,1,,

s2tb3,19,,,,,,Thomas I.,,,"Selections Illustrating the History of Greek Mathematics",,,,Cambridge Mass.,1939,,,,1,,

s2tb4,19,,,,,,Todhunter I.,,,"Algebra for Beginners",,,,Cambridge,1863,,,,1,,

s2tb5,20,,,,,,Trevisan V.,Wang P.,,Practical factorization of univariate polynomials over finite fields in "Proc. 1991 Internat. Symp. Symbolic Algebraic Comput." ed. S.M. Watt,,,ACM Press,,1991,22,31,,1,,

s2tb6,19,,,,,,Tropfke J.,,,"Geschichte der Elementarmathematik III",,,,Berlin,1930,,,,1,,

s2tb7,19,,,,,,Pai-chi Tsou,,,"Su-pu Hsi-t'ao",,,,,1868,,,,1,,

s2uj1,21,,,,,,Ullman J.L.,,,A class of weight functions that admit Tchebycheff quadrature,Michigan Math. J.,13,,,1966,417,423,,1,,

s2uj2,19,,,,,,Ungar A.A.,,,A unified method for solving quadratic cubic and quartic equations,Arbstracts of Amer. Math. Soc.,3,,,1982,290,290,,1,,

s2uj3,28,,,,,,Vâjâitu V.,Zaharescu A.,,Ilyeff's conjecture on a corona,Bull. London Math. Soc.,25,,,1993,49,54,,1,,

s2uj4,15,,,,,,Vallas A.,,,Note on Numerical Equations,Amer. Math. Monthly,3,,,1860,10,18,,1,,

s2uj5,31,,,,,,Valtinowsky,,,Einiges über die Beerechnung der reellen Wurzelne numerischer Gleichungen mittelst ohne Ende fortlaufender Reihen,J. Reine Angew. Math.,33,,,1846,164,173,,1,,

s2uj6,4,13,,,,,Valz J.E.B.,,,De la résolution des équations numériques par l'abaissement des puissances des racines et le rapprochement en résultant dans leur limites,C.R. Acad. Sci. Paris,41,,,1855,685,687,,1,,

s2uj7,31,,,,,,Valz J.E.B.,,,Essai de la résolution des équations par les séries et les logarithmes,C.R. Acad. Sci. Paris,49,,,1859,705,711,,1,,

s2uj8,21,,,,,,Van Assche W.,,,Invariant zero behaviour for orthogonal polynomials on compact sets of the real line,Bull. Soc. Math. Belge Ser. B,38,,,1986,1,13,,1,,

s2uj9,21,,,,,,Van Assche W.,,,Norm Behaviour and Zero distribution for Orthogonal Polynomials with Non-Symmetric Weights,Constr. Approx.,5,,,1989,329,345,,1,,

s2uj10,21,,,,,,Van Assche W.,Vanherwegen I.,,Quadrature formulas based on rational interpolation,Math. Comp.,63,,,1993,765,783,,1,,

s2uj11,20,,,,,,van der Waerden B.L.,,,Noch eine Bemerkung zu der Arbeit zur Arithmetik der Polynome von U. Wegner,Math. Ann.,109,,,1934,679,680,,1,,

s2uj12,13,,,,,,van der Waerden B.L.,,,Die Seltenheit der reduziblen Gleichungen und der Gleichungen mit Affekt,Monatsh. Math.,43,,,1936,133,147,,1,,

s2uj13,25,,,,,,van der Waerden B.L.,,,Die Algebra seit Galois,Jahresber. Deutsch. Math.-Verein.,68,,,1966,155,165,,1,,

s2uj14,21,,,,,,Van Doorn E.A.,,,On orthogonal polynomials with positive zeros and the associated kernel polynomials,J. Math. Anal. Appl.,113,,,1986,441,450,,1,,

s2uj15,20,29,,,,,Vandiver H.S.,,,Algorithms for the solution of the quadratic congruence,Amer. Math. Monthly,36,,,1929,83,86,,1,,

s2uj16,20,,,,,,van Oorschot P.C.,Vanstone S.A.,,A geometric approach to root finding in GF(q^m),IEEE Trans. Inform. Theory,35,,,1989,444,453,,1,,

s2uj17,19,,,,,,Vanson,,,Note sur une limite des racines des équations du troisième et du quatrième degré,Nouv. Ann. Math.,11,,,1852,60,61,,1,,

s2uj18,10,,,,,,Vardulakis A.I.G.,Stoyle P.N.R.,,Generalized resultant theorem,J. Inst. Math. Appl.,22,,,1978,331,335,,1,,

s2uj19,21,,,,,,Varga R.,,,Asymptotics for the zeros and poles of normalized Padé approximations to e^z,Numer. Math.,68,,,1994,169,185,,1,,

s2uj20,16,,,,,,Vassiliev V.A.,,,Cohomology of braid groups and complexity of algorithms,Funct. Anal. Appl.,22 No. 3,,,1988,15,24,,1,,

s2uj21,19,,,,,,Vériot,,,Mémoire sur la résolution de l'équation du troisième degré,C.R. Acad. Sci. Paris,60,,,1865,556,557,,1,,

s2uj22,21,,,,,,Vértesi P.,,,On the zeroes of generalized Jacobi polynomials,Ann. Numer. Math.,4,,,1997,561,577,,1,,

s2uj23,17,,,,,,Vijay M.,,,Fault-tolerant systolic evaluation of polynomials and exponentials of polynomials for equispaced arguments using time redundancy,Intern. J. High-Speed Computing,7,,,1995,351,363,,1,,

s2uj24,18,,,,,,Vitasse,,,Note sur la limite supérieure des racines négatives déduites de la formule aux différences de Newton,Nouv. Ann. Math. Ser. 2,18,,,1879,213,215,,1,,

s2uj25,19,,,,,,Vogel K.,,,Zur Berechnung der quadratischen Gleichungen bei den Babyloniern,Unterrichtsblatter fur Mathematik und Naturwiss.,39,,,1933,76,81,,1,,

s2uj26,20,,,,,,von zur Gathen J.,,,Factoring polynomials and primitive elements for special primes,Theoret. Comput. Sci.,52,,,1987,77,89,,1,,

s2uj27,20,,,,,,von zur Gathen J.,Shoup V.,,Computing Frobenius maps and factoring polynomials,Computational Complexity,2,,,1992,187,224,,1,,

s2uj28,17,,,,,,von zur Gathen J.,Strassen V.,,Some polynomials that are hard to compute.,Theoret. Comput. Sci.,11,,,1980,331,335,,1,,

s2ub1,13,,,,,,Umemura H.,,,Resolution of Algebraic Equations by Theta Constants in "Tata Lectures on Theta II Chap. 3" D. Mumford ed.,,,Birkhauser,Boston,1984,261,272,,1,,

s2ub4,20,,,,,,Uspenky J.V.,Heaslett M.A.,,"Elementary Number Theory",,,McGraw-Hill,New York,1989,,,,1,,

s2ub5,19,29,,,,,van der Waerden B.L.,,,"Geometry and Algebra in Ancient Civilizations",,,Springer-Verlag,,1983,,,,1,,

s2ub6,16,,,,,,Vassiliev V.A.,,,"Complements of Discriminants of Smooth Maps: Topology and Applications; Translations of Math. Monographs Vol. 98",,,,Providence RI,1994,,,,1,,

s2ub7,16,,,,,,Vassiliev V.A.,,,Topological Complexity of Root-Finding Algorithms in "The Mathematics of Numerical Analysis" Eds. J. Renegar et al,,,Amer. Math. Soc.,,1996,831,856,,1,,

s2ub8,19,25,,,,,Verriest G.,,,"Evariste galois et la theorie des équations algébriques",,,Gauthier-Villars,Paris,1951,,,,1,,

s2ub9,2,7,29,,,,Vieille J.,,,"Théorie générale des approximations numériques",,,Mallet-Bachelier,Paris,1854,,,,1,,

s2ub10,19,25,,,,,Vogt H.,,,"Leçons sur la Résolution Algébrique des équations",,,,Paris,1895,,,,1,,

s2ub12,19,,,,,,Von der Schulenburg A.,,,"Die Auflösung der Gleichungen funften Grades",,,H.W. Schmidt,Halle,1861,,,,1,,

s2ub13,31,,,,,,Von Mangoldt H.,,,"Ueber die Darstellung der Wurzeln einer dreigliedrigen algebraischen Gleichung durch unendliche Reihen",,,,Berlin,1878,,,,1,,

s2ub14,20,,,,,,von zur Gathen J.,Kozen D.,Landau S.,Functional decomposition of polynomials in "28th Symposium on Foundations of Computer Science",,,ACM,,1987,127,131,,1,,

s2ub15,20,,,,,,von zur Gathen J.,Shoup V.,,Computing Frobenius maps and factoring polynomials in "Proc. Twenty-fourth Ann. ACM Symp. Theor. Comput.",,,,,1992,97,105,,1,,

s2wj1,10,,,,,,Walecki,,,Démonstration du théorème d'Alembert,Nouv. Ann. Math. Ser. 3,2,,,1883,241,248,,1,,

s2wj2,3,,,,,,Wang D.,Zhao F.,,Complexity analysis of a process for simultaneously obtaining all zeros of polynomials,Computing,43,,,1990,187,197,,1,,

s2wj3,3,,,,,,Wang D.,Zhao F.,,On the determination of the safe initial approximation for the Durand-Kerner algorithm,J. Comput. Appl. Math.,38,,,1991,447,456,,1,,

s2wj4,2,3,,,,,Wang D.,Zhao F.,,The theory of Smale's point estimation and its applications,J. Comput. Appl. Math.,60,,,1995,253,269,,1,,

s2wj5,32,,,,,,Wang Z.,,,A constructive approach to zero distribution of a class of continuous functions,Science in China Ser. A,32,,,1989,1281,1288,,1,,

s2wj6,20,,,,,,Ward M.,,,On the factorization of polynomials to a prime modulus,Ann. Math. Ser. 2,36,,,1935,870,874,,1,,

s2wj7,19,,,,,,Waring E.,,,On the General Resolution of Algebraic Equations,Philos Trans. Roy. Soc. London,14,,,1779,487,495,,1,,

s2wj8,25,,,,,,Weber H.,,,Die allgemeinen Grundlagen der Galois'chen Gleichungstheorie,Math. Ann.,43,,,1893,521,549,,1,,

s2wj9,21,,,,,,Weddle T.,,,A new and easy method of approximating to the unreal roots of trinomial equations,The Mathematician,3,,,1849,285,289,,1,,

s2wj10,20,,,,,,Wegner U.,,,Zur Arithmetik der Polynome,Math. Ann.,105,,,1931,628,631,,1,,

s2wj11,1,2,,,,,Wiethoff A.,,,Enclosing all zeros of a nonlinear function on a parallel computer system,Z. Angew. Math. Mech.,76 Supp. 1,,,1996,585,586,,1,,

s2wj12,27,,,,,,Wilkins J.E. Jr.,,,An asymptotic expansion for the expected number of real zeros of a random polynomial,Proc. Amer. Math. Soc.,103,,,1988,1249,1258,,1,,

s2wj13,20,29,,,,,Williams H.C.,Hardy K.,,A refinement of H.C. Williams qth root algorithm,Math. Comp.,61,,,1993,475,483,,1,,

s2wj14,14,20,,,,,Williams H.C.,Zarnke C.R.,,Some algorithms for solving a cubic congruence modulo p,Utilitas Math.,6,,,1974,285,306,,1,,

s2wj15,20,19,,,,,Williams K.S.,,,Note on cubics over GF(2ⁿ) and GF(3ⁿ),J. Number Theory,7,,,1975,361,365,,1,,

s2wj16,19,25,,,,,Wilson G.,,,Essay on the Resolution of Algebraic Equations,Philos. Trans. Roy. Soc. London,89,,,1799,265,304,,1,,

s2wj17,19,,,,,,Woepcke F.,,,Addition à la discussion de deux méthodes arabes....,J. Math. Pures Appl.,19,,,1854,153,176,,1,,

s2wj18,19,,,,,,Woepcke F.,,,Sur la construction des équations du quatrième degré,J. Math. Pures Appl. Ser. 2,8,,,1863,57,70,,1,,

s2wj19,29,,,,,,Wong W.F.,Goto E.,,Division and square rooting using a split multiplier,Electron. Lett.,28,,,1992,1758,1759,,1,,

s2wj20,31,,,,,,Woolhouse W.S.B.,,,On General Numerical Solution,Proc. London Math. Soc.,2,,,1868,75,85,,1,,

s2xb1,2,18,29,,,,Xavier A.,,,"Théorie des approximations numériques et du calcul abrégé",,,Gauthier-Villars,Paris,1909,,,,1,,

s2xb2,3,,,,,,Yamamoto T.,,,SOR-like Methods for the Simultaneous Determination of Polynomial Zeroes in "Numerical Methods and Error Bounds" ed G. Alefeld and J. Herzberger,,,Akademie Verlag,,1996,287,295,,1,,

s2xb3,3,12,,,,,Yamamoto T.,Kanno S.,Atanassova L.,Validated computation of polynomial zeros by the Durand-Kerner method in "Topics in Validated Computations" ed J. Herzberger,,,North-Holland,Amsterdam,1994,27,62,,1,,

s2xb4,19,29,,,,,Young J.R.,,,"An Elementary Treatise on Algebra",,,J. Souter,London,1826,,,,1,,

s2xb5,10,18,19,,,,Young J.R.,,,"The analysis and solution of cubic and biquadratic equations",,,,London,1842,,,,1,,

s2xb6,10,,,,,,Young J.R.,,,"Researches Respecting the Imaginary Roots of Numerical Equations",,,Souter and Law,London,1844,,,,1,,

s2xb7,10,19,,,,,Young J.R.,,,"The Analysis of Numerical Equations",,,C.C. Spiller,London,1850,,,,1,,

s2xb8,19,29,,,,,Youschkevitch A.P.,,,"Les mathematiques arabes VIIIe-XVe siècles" Trans. M. Cazanave and K. Jaouiche,,,,Paris,1976,,,,1,,

s2xb9,19,,,,,,Zeuthen H.G.,,,"Notes sur l'Histoire des Mathématiques Vol. 2",,,,,1893,303,380,,1,,

s2xb10,19,,,,,,Zeuthen H.G.,,,"Histoire des Mathematiques dans l'Antiquité et le Moyen-Age",,,Gauthier-Villars,Paris,1902,,,,1,,

s2xb11,19,,,,,,Zeuthen H.G.,,,"Geschichte der Mathematik im XVI u XVII Jahrhundert",,,Johnson reprint,,1966,,,,1,,

s2xb12,20,,,,,,Zimmer H.G.,,,"Computational Problems Methods and Results in Algebraic Number Theory",,,Springer-Verlag,Berlin,1972,,,,1,,

s2xb13,10,18,20,,,,Zippel R.,,,"Effective Polynomial Computation",,,Kluwer,Dordrecht,1993,,,,1,,

s2xb14,2,,,,,,Zoltan S.,,,Newton-parabola combined method for solving equations in "IMACS '91" eds. R. Vichnevetsky and J.J.H. Miller,,,,,1991,217,218,,1,,

s2wb1,1,15,,,,,Wagner W.,,,"Bestimnung der Genuigkeit; welche die Newton'sche Methode zur Berechnung der Wurzeln darbieter; für Gleichung mit einer und mehreren Unbekannten",,,,Leipzig,1860,,,,1,,

s2wb2,19,,,,,,Wang Hs'iao-t'ung,,,"Ch'i-ku Suan-ching",,,,,625,,,,1,,

s2wb3,19,25,,,,,Weber H.,,,"Elliptische Functionen und Algebrische Zahlen",,,Vieweg,,1891,,,,1,,

s2wb4,31,,,,,,Westphal,,,"Evolutio radicum aequationum algebraicarum eternis terminis constantium in series infinitas",,,,Gottingen,1850,,,,1,,

s2wb5,19,,,,,,Wiegands A.,,,"Algebraische Analysis",,,,Halle,1853,57,75,,1,,

s2wb6,11,,,,,,Willems J.L.,,,"Stability Theory of Dynamical Systems",,,Nelson,London,1970,,,,1,,

s2wb7,20,29,,,,,Williams H.C.,,,Some Algorithms for Solving x^q ≡ N mod (p) in "Proc. Third Southeastern Conf. on Combinatorics Graph Theory and Computing",,,Utilitas Math.,Winnipeg Man.,1972,451,462,,1,,

s2wb9,19,,,,,,Woepcke F.,,,"L'Algèbre d'Omar Alkhayyami",,,,Paris,1851,,,,1,,

s2wb10,19,,,,,,Woepcke F.,,,"Recherches sur l'histoire des sciences mathematiques chez les orientaux",,,,Paris,1855,,,,1,,

,29,0,0,0,0,0,Lam, L.Y.,,,On the Existing Fragments of Yang Hui's 'Hsiang chieh suan fa',Arch. Hist. Exact. Sci.,6,,,1969,82,88,Finds 4th root by Horner's method,1,0,

s2xj16,3,,,,,,Zheng S.,Sun F.,,Some simultaneous iterations for finding all zeroes of a polynomial with high order convergence,Appl. Math. Comp.,99,,,1999,233,240,,1,,

s2xj17,20,,,,,,Zierler N.,,,A Conversion algorithm for logarithms on GF(2ⁿ),J. Pure Appl. Algebra,4,,,1974,353,356,,1,,

s2xj18,20,,,,,,Zsigsmundy K.,,,über die Anzahl derjenigen ganzen ganzahligen Functionen n^ten Grades von x; welche in Bezug auf einen gegebenen Primzahlmodul eine vorgeschriebene Anzahl von Wurzeln besitzen,Sitz. Akad. Wiss. Wein Math. Nat. Kl.; Wein,103,,,1894,135,144,,1,,

s2xj19,29,,,,,,Zurawski J.H.P.,Gosling J.B.,,Design of a high-speed square root multiply and divide unit,IEEE Trans. Comput.,36,,,1987,13,23,,1,,

,26,0,0,0,0,0,Malajovich, G.,,,Condition Number Bounds for Problems with Integer Coefficients,J. Complexity,16,,,2000,529,551,Condition number is ≤ 2^2d²-2d^2d(max|f_i|)^2d² where d = degree and f_i are coefficients.,1,0,

,2,5,32,0,0,0,Yakoubsohn, J.-C.,,,Finding a Cluster of Zeros of Univariate Polynomials,J. Complexity,16,,,2000,603,638,Uses homotopy, Newton's method, and Rouché's theorem.,1,0,

,10,0,0,0,0,0,Roy, M.F.,,,Basic algorithms in real algebraic geometry and their complexity: from Sturm's theorem to the existential theory of the reals, in "Lectures on Real Geometry in Memoriam Mario Raimondo" ed F. Broglia,,,Walter de Gruyter,Berlin,1996,0,0,Get Page nos.,1,0,

,21,0,0,0,0,0,Pasquini, L.,,,Accurate computation of the zeros of the generalized Bessel polynomials,Numer. Math.,86,,,2000,507,538,Seems to be the only algorithm giving accurate solution.,1,0,

,25,0,0,0,0,0,Sen, A.,,,The Fundamental Theorem of Algebra-Yet Another Proof,Amer. Math. Monthly,107,,,2000,842,843,uses fact that Image(P) = C,1,0,

,19,0,0,0,0,0,Rodet, L.,,,Leçons de Calcul d'Âryabhata,,,Imprimerie Nationale,Paris,1879,0,0,Treats quadratic formula,1,0,

,10,0,0,0,0,0,Karmarkar, N.K.,Lakshman, Y.N.,,On Approximate GCD's of Univariate Polynomials,J. Symb. Comput.,26,,,1998,653,666,Considers finding approximate common divisors for inexactly specified polynomials.,1,0,

,26,0,0,0,0,0,Lihong, Z.,Wenda, W.,,Nearest Singular Polynomial,J. Symb. Comput.,26,,,1998,667,675,Considers nearest singular polynomial with a zero of multiplicity ≥ 2.,1,0,

,10,0,0,0,0,0,Beckermann, B.,Labahn, G.,,When are two Numerical Polynomials Relatively Prime?,J. Symb. Comput.,26,,,1998,677,689,Considers the question of when 2 polynomials are relatively prime, even after small perturbations of the coefficients.,1,0,

,10,0,0,0,0,0,Beckermann, B.,Labahn, G.,,A Fast and Numerically Stable Euclidean-Like Algorithm for Detecting Relatively Prime Numerical Polynomials,J. Symb. Comput.,26,,,1998,691,714,Considers the question of when 2 polynomials are relatively prime, even after small perturbations of the coefficients.,1,0,

,3,0,0,0,0,0,Bini, D.A.,Fiorentino, G.,,Design, analysis, and implementation of a multiprecision polynomial rootfinder.,Numer. Alg.,23,,,2000,127,173,Uses simultaneous iteration method of Ehrlich-Aberth, with cluster analysis to speed convergence for multiple roots.,1,0,

,17,0,0,0,0,0,Bini. D.A.,Fiorentino, G.,,On the parallel evaluation of a sparse polynomial at a point.,Numer. Alg.,20,,,1999,323,329,Requires log n parallel steps with n/2+1 processors, n+log(n+1)-1 mults & n adds. If sparse, i.e. has k< ,10,0,0,0,0,0,Coste, M.,Roy, M.-F.,,Thom's lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets.,J. Symb. Comput.,5,,,1988,121,129,Considers sign of certain other polynomials at roots of a given polynomial (all with integer coefficients).,1,0,

,2,0,0,0,0,0,Bachman G.,,,Introduction to p-adic Numbers and Valuation Theory,,,Academic Press,New York and London,1964,0,0,Proves conditions for convergence of Newton's method.,1,0,

,20,,,,,,Agou S.,,,Sur la factorisation des polynômes f(X^{p^2r}- aX^{p^r}-bX) sur une corps fini F_p^s,J. Number Theory,12,,,1980,447,459,,1,,

,25,,,,,,Abel N.H.,,,"Collected Works Vol. 1",,,,Christiana,1881,28,34,see also pp66-87; 478; and Vol. 2 217-244,1,,

,19,,,,,,Anon,,,Irreducible Case in " Penny Cyclopaedia Vol.13",,,Charles Knight,London,1839,38,39,,1,,

,2,10,13,19,25,,Anon,,,Theory of Equations in "Penny Cyclopaedia Vol.24,,,,London,1842,339,342,,1,,

,20,,,,,,Agou S.,,,Factorisation sur un corps fini F_pⁿ des polynômes composés f(X^p-aX) lorsque f(X) est un polynôme irréductible de F_pⁿ[X],J. Number Theory,9,,,1977,229,239,,1,,

,29,0,0,0,0,0,Kuki H.,Ascoly J.,,FORTRAN Extended-Precision Library,IBM Systems J.,10,,,1971,39,61,Covers square-root function.,1,0,

,29,0,0,0,0,0,Hull T.E.,Abrham A.,,Properly Rounded Variable Precision Square-Root,ACM Trans. Math. Software,11,,,1985,229,237,Title says it.,1,0,

,20,0,0,0,0,0,Knopfmacher J.,Knopfmacher A.,,Counting irreducible factors of polynomials over a finite field.,Discrete Math.,112,,,1993,103,118,,1,0,

,20,0,0,0,0,0,Kaltofen E.,Musser D.R.,Saunders B.D.,A generalized class of polynomials that are hard to factor.,SIAM J. Comput.,12,,,1983,473,485,Defines polynomials which make the Berlekamp-Hensel factorization take exponential time.,1,0,

,17,0,0,0,0,0,Lakshman Y.N.,Saunders B.D.,,On computing sparse shifts for univariate polynomials. In "ISSAC '94 Proc. Internat. Symp. Symbolic Algebraic Comput." (ed. J. von zur Gathen and M. Giesbrecht),,,ACM Press,New York,1994,108,113,,1,0,

,10,0,0,0,0,0,Schönhage A.,Vetter E.,,A New Approach to Resultant Computations and Other Algorithms with Exact Divisions. In Algorithms. ESA '94 (Utrecht 1994) ed. J. v. Leeuwen. (LNCS 885),,,,,1994,448,459,Fast methods for resultants.,1,0,

,19,25,0,0,0,0,Fauvel J.,Gray J.,,The history of mathematics: a reader.,,,Macmillan,,1987,0,0,Original writings eg. Arabs on quadratics, cubics, Gauss on existence.,1,0,

,29,0,0,0,0,0,Cohen A.M.,,,Approximating square roots and cube roots.,Math. Gaz.,67,,,1983,221,223,Shows that a method of Grant's is equivalent to Newton's method.,1,0,

,18,0,0,0,0,0,Elsener L.,,,A remark on simultaneous inclusions of the zeros of a polynomial by Gerschgorin's theorem.,Numer. Math.,21,,,1973,425,427,Deduces a posteriori bounds,1,0,

,20,0,0,0,0,0,Schwarz St.,,,On the reducibility of polynomials over a finite field.,Quart. J. Math. Oxford (Ser. 2),7,,,1956,110,124,,1,0,

,19,0,0,0,0,0,Sullivan J.W.N.,,,The History of Mathematics in Europe.,,,Oxford Univ. Press,,1925,0,0,Brief history of Cubic and Quartic,1,0,

,19,29,0,0,0,0,Lam, L.Y.,,,A Critical Study of the Yang Hui Suan Fa; A Thirteenth-Century Chinese Mathematical Treatise.,,,,,,0,0,Medieval Chinese roots and quadratics.,1,0,

,19,25,0,0,0,0,Fink K.,,,A Brief History of Mathematics. Trans. W.W. Beman and D.E. Smith.,,,Paul Kegan,London,1900,0,0,History of low degree polynomials; non-solubility by radicals of higher degree; solution by elliptic integrals.,1,0,

,1,0,0,0,0,0,Herceg D.,,,"An algorithm for localization of polynomial zeros", in Proc. VIII Intern. Conf. On Logic and Comp. Science.,,,Novi Sad,,1997,67,75,2-dimensional bisection method.,1,0,

,1,2,0,0,0,0,Pan V.Y.,,,New techniques for approximating complex polynomial zeros, in "5th Annual ACM-SIAM Sympos. on Discrete Algorithms",,,ACM Press,New York,1994,260,270,Uses 2-D bisection method, proximity test, and improved Newton's method.,1,0,

,10,25,0,0,0,0,Bôcher,,,Introduction to Higher Algebra,,,,,1907,0,0,Treats existence and GCD's,1,0,

,25,0,0,0,0,0,Bôcher,,,Gauss's "Third proof of the fundamental theorem of algebra",Bull. Amer. Math. Soc.,1,,,1895,205,,Relates fundamental theorem to Theory of Functions and Potential Theory,1,0,

,23,0,0,0,0,0,Baker,,,A balance for the solution of algebraic equations,Amer. Math. Monthly,11,,,1904,224,224,Describes a mechanical method,1,0,

,2,3,12,0,0,0,Petkovic M.S.,Herceg D.D.,Ilic S.M.,Point Estimation Theory and its Applications,,,Inst. Math.,Novi Sad,1997,0,0,Treatment of Newton and Simultaneous Methods,1,0,

,5,0,0,0,0,0,Kravanja, K.,Van Barel, M.,Haegemans, A.,On Computing Zeros and Poles of Mereomorphic Functions, in "Computational Methods and Function Theory 1997", ed. N. Papamichael et al,,,World Scientific,Singapore,1999,359,369,Based on Contour Integration and Formal Polynomials,1,0,

,29,0,0,0,0,0,Curtze, M.,,,Petri Philomeni de Dacia in Algorismum Vulgarem Johannis de Sacrobosco Commentarius,,,A.F. Host,,1897,0,0,Mediaeval Treatment of Square and Cube Roots,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Teoria Generale delle Equazioni, in cui si Dimostra Impossibile la Soluzione Algebraica delle Equazioni Generali di Grado Superiore al Quarto, in "Opere Matematiche Vol. 1", ed. E. Bortolotti,,,,,1915,0,0,,1,0,

,11,0,0,0,0,0,Gemignani, L.,,,Computing a Hurwitz Factorization of a Polynomial,J. Comput. Appl. Math.,126,,,2000,369,380,Factors into f(z) g(z) where f(z) has only roots with negative real parts.,1,0,

,15,0,0,0,0,0,Kalantari, B,,,Generalization of Taylor's Theorem and Newton's Method via a New Family of Determinantal Interpolation Formulas and its Applications,J. Comput. Appl. Math.,126,,,2000,287,318,,1,0,

,21,28,0,0,0,0,Dimitrov, D.K.,Ronveaux, A.,,Inequalities for Zeros of Associated Polynomials and Derivatives of Orthogonal Polynomials,Appl. Numer. Math.,36,,,2001,321,331,Considers interleaving of roots.,1,0,

,20,0,0,0,0,0,Panaitapol, L.,Stefanescu, D.,,Some Criteria for Irreducibility of Polynomials,Bull.Math Soc Sc Math Roumainie,29,,,1985,69,74,,1,0,

,13,2,0,0,0,0,Murphy, R.V.W.,,,Iterative Solutions of F(x)=0,Math. Gaz.,84,,,2000,493,498,Discusses variations on direct iteration and Newton,1,0,

,17,0,0,0,0,0,Barrio, R.,,,Parallel Algorithms to Evaluate Orthogonal Polynomial Series,SIAM J. Sci. Comput.,21,,,2000,2225,2239,Presents 4 algorithms for evaluation, in MIMD, of polynomials written as finite series of orthogonal polynomials.,1,0,

,18,20,0,0,0,0,Lawton, W.,,,Asymptotic Properties of Roots of Polynomials, in "Proc. Seventh Iranian Mathematics Conference", ed. M. Toomanian,,,,,1977,212,217,Concerns roots of integer polynomials near the unit circle,1,0,

,1,2,0,0,0,0,Herzberger, J.,,,Mathematische Zinsberechnung,,,Spectrum Akad. Verlag,Berlin,1995,0,0,Covers bisection, Newton.,1,0,

,20,0,0,0,0,0,Mann, M.F.J.,,,,Mathematical Questions & Sols. From The Educ Times,56,,,1892,124,127,,1,0,

,28,0,0,0,0,0,Andrews, P.,,,Where not to find the critical points of a polynomial -Variation on a Putnam theme,Amer. Math. Monthly,102,,,1995,155,158,Shows how roots of derivative are bounded away from roots of a polynomial.,1,0,

,5,0,0,0,0,0,Katz, I.N.,Ying, X.,,A reliable principle algorithm to find the number of zeros of an analytic function in a bounded domain.,Numer. Math.,53,,,1988,143,163,,1,0,

,19,0,0,0,0,0,Bombelli,,,L'algebra parte maggiore dell'arithmetica,,,,Bologna,1572,0,0,,1,0,

,1,2,3,12,0,0,Alefeld, G.,Herzberger, J.,,Introduction to Interval Computations. Chap. 7,,,Academic Press,New York,1983,0,0,,1,0,

,3,18,12,25,0,0,Rump, S.M.,,,Solving Algebraic Problems with High Accuracy in "A New Approach to Scientific Computation" eds. U. Kulisch, W.L. Miranker,,,Academic Press,New York,1983,51,120,Considers Interval Methods, including simultaneous,1,0,

,19,0,0,0,0,0,Ciotti, J.,,,Some Methods for Constructing the Parabola,Math. Teacher,67,,,1974,428,430,,1,0,

,19,0,0,0,0,0,Smith, Brother Albertus,,,A "Stencil Method" fpr Solving Quadratics of the Type ax² + bx + c = 0 That have Real Roots,Math. Teacher,72,,,1979,661,667,Geometric method for quadratic,1,0,

,10,0,0,0,0,0,Campbell, G.,,,A Demonstration of the Cartesian Rule for Determining the Number of Positive and Negative Roots in any adfected Equation,,,J.Wilford,London,1729,,0,Rule for determining how many roots complex, and bounding them.,1,0,

,25,0,0,0,0,0,Campbell, G.,,,A Method for Determining the Number of impossible Roots in adfected Aequations,Philos. Trans. Roy. Soc. London,35,,,1728,515,531,Rule for determining how many roots complex and bounding them,1,0,

,19,0,0,0,0,0,Adamo, M.,,,La matematica nell'antica Cina,Osiris,15,,,1968,175,195,Brief mention of cubic in China.,1,0,

,19,29,0,0,0,0,Ang Tian-Se,Swetz, F.J.,,A brief chronological and bibliographic guide to the History of Chinese Mathematics,Historia Math.,11,,,1984,39,56,,1,0,

,19,0,0,0,0,0,De Morgan, A.,,,Elements of algebra preliminary to the differential calculus,,,John Taylor,London,1835,0,0,Treats quadratics.,1,0,

,19,0,0,0,0,0,Tannery, P.,,,Diophanti Alexandrini; Opera omnia cum Graecis Commentariis,,,,Lipsiae,1893,0,0,Treats some quadratics.,1,0,

,20,0,0,0,0,0,Brawley, J.,Schnibben, G.,,Infinite Algebraic Extensions of Finite Fields,Contemp. Math,95,Amer. Math. Soc.,,1989,0,0,Considers irreducible polynomials.,1,0,

,29,0,0,0,0,0,Schönborn,,,Über die Methode, nach die alten Griechen (insbesondere Archimedes und Heron) Quadratwurzeln berechnet haben,Zeit. Math.Phys. (hist.-lit Abt.),28,,,1883,169,178,Treats square roots among ancient Greeks,1,0,

,0,0,0,0,0,0,Flammang, V.,,,Comparison de deux mesures de polynômes,Canad. Math. Bull.,38(4),,,1995,438,444,Considers bounds on measure of P (= product of roots >1),1,0,

,27,0,0,0,0,0,Samal G.,,,Number of real zeros of a random algebraic polynomial,Indian J. Math,20,,,1978,225,232,If coefficients have characteristic function e^{-C|t|^α}, then the number of real roots is usually ≥ ε log n, where ε_n→ 0 but ε_nlog n→∞,1,0,

,19,0,0,0,0,0,Neugebauer O.,,,Beitrage zur Geschichte der babylonischen Arithmetik,Quellen u.Studien z. Geschichte der Math.,1,,,1930,120,130,Babylonian treatment of quadratics,1,0,

,19,0,0,0,0,0,Neugebauer O.,,,Studien zur Geschichte der antiken Algebra I,Quellen u. Studien z. Geschichte der Math.,2,,,1932,1,27,Babylonian treatment of quadratics,1,0,

,20,0,0,0,0,0,Menezes, A.J.,Blake, I.F.,et al,Applications of finite fields,,,Kluwer Acad. Publishers,Dordrecht,NL,1993,0,0,Chapter on factoring polynomials over finite fields,1,0,

,29,0,0,0,0,0,Cardan,,,Practica Arithmetice,,,,Milan,1539,0,0,,1,0,

,19,29,0,0,0,0,Lam, Lay-Yong,,,The geometrical basis of the Ancient Chinese square-root method.,Isis,61,,,1970,92,102,Chinese could extract roots before West.,1,0,

,29,0,0,0,0,0,Simons, M.,,,Geschichte der Mathematik im Altertum,,,,Berlin,1909,138,138,Ancient treatment of roots.,1,0,

,10,17,0,0,0,0,Borowczyk J.,,,Sur la vie et l'oeuvre de François Budan (1761-1840),Historia Math.,18,,,1991,129,157,Improvement on Descartes' rule,1,0,

,19,0,0,0,0,0,Chasles M.,,,Sur l'époque où l'algèbre a été introduite en Europe,C. R. Acad. Sci. Paris,13,,,1841,497,524,Includes history of quadratic,1,0,

,19,0,0,0,0,0,Chasles M.,,,Sur les expressions res et census. Et sur le nom de la science, Algebra et Almuchabala,C.R. Acad. Sci. Paris,13,,,1841,601,628,Includes history of quadratic,1,0,

,2,10,18,19,25,0,Capelli A.,,,Istituzioni di analisi algebrica,,,,Naples,1902,0,0,Treats Newton, Low-Order, Existence, Fourier-Budan, Sturm, Bounds.,1,0,

,19,25,0,0,0,0,Maracchia S,,,Da Cardana a Galois,,,,Feltrinelli,1979,0,0,Treats cubic, quartic, and existence.,1,0,

,19,0,0,0,0,0,Coolidge J.L.,,,The Mathematics of Great Amateurs.,,,Clarendon Press,London,1949,0,0,Chapter on early study of cubics.,1,0,

,19,0,0,0,0,0,Ho, Peng Yoke,,,The Lost Problems of the Chang Ch'iu-chien Suan Ching, a fifth-century Chinese Mathematical Manual.,Orïens Extremus.,12,,,1965,37,37,Early Chinese quadratic solution.,1,0,

,20,0,0,0,0,0,Carmichael R.D.,,,Theory of Numbers and Diophantine Analysis.,,,Dover Publications,New York,1959,0,0,Treats polynomial congruences.,1,0,

,5,0,0,0,0,0,Ioakimidis N. I.,,,Application of the generalized Siewert-Burniston method to locating zeros and poles of meromorphic functions.,Z. Angew. Math. Phys.,36,,,1985,733,742,Uses argument principle,1,0,

s2wb11,19,,,,,,Woepcke F.,,,"Extrait du Fakhri. Traité d'Algèbre par Bekr Mohammed ben Alhacan Alkarkhi",,,Georg Olms,Hildesheim,1982,,,,1,,

s2wb12,1,10,18,19,29,,Wood J.,,,"The Elements of Algebra",,,,Cambridge,1830,,,,1,,

s2wb13,1,2,7,,,,Woodford C.,,,"Solving Linear and Non-Linear Equations",,,Ellis Horwood,New York,1992,,,,1,,

s2wb14,16,,,,,,Wo\'{z}niakowski H.,,,Overview of Information-based Complexity in "The Mathematics of Numerical Analysis" Eds. J. Renegar et al,,,Amer. Math. Soc.,,1996,915,927,,1,,

s2xj1,21,,,,,,Xu Y.,,,A characterization of positive quadrature formulae,Math. Comp.,62,,,1994,703,718,,1,,

s2xj2,5,,,,,,Yakoubsohn J.-C.,,,Approximating the zeros of analytic functions by the exclusion algorithm,Numerical Algorithms,6,,,1994,63,88,,1,,

s2xj3,3,,,,,,Yamagishi Y.,,,Stable spiral orbits of SOR Durand-Kerner's method applied to the equation x^d = 0,J. Comput. Appl. Math.,82,,,1997,465,475,,1,,

s2xj4,2,15,,,,,Yau L.,Ben-Israel A.,,The Newton and Halley Methods for Complex Roots,Amer. Math. Monthly,105,,,1998,806,818,,1,,

s2xj5,19,25,,,,,Young G.P.,,,Principles of the Solution of Equations of the Higher Degrees; with Applications,Amer. J. Math.,6,,,1884,65,102,,1,,

s2xj6,19,25,,,,,Young G.P.,,,Resolution of Solvable Equations of the Fifth Degree,Amer. J. Math.,6,,,1884,103,114,,1,,

s2xj7,19,25,,,,,Young G.P.,,,Solution of Solvable Irreducible Quintic Equations; without the aid of a Resolvent Sextic,Amer. J. Math.,7,,,1885,170,177,,1,,

s2xj8,19,25,,,,,Young G.P.,,,Solvable Irreducible Equations of Prime Degree,Amer. J. Math.,7,,,1885,271,278,,1,,

s2xj9,18,,,,,,Young J.R.,,,New Criteria for the Imaginary Roots of Equations,Phil. Mag.,22,,,1843,186,188,see also ibid 23 (1843) 450-452,1,,

s2xj10,25,,,,,,Young J.R.,,,Remarks on the problem of the general solution of algebraic equations,Mechanics' Magazine,48,,,1848,101,102,,1,,

s2xj11,2,,,,,,Ypma T.J.,,,Historical developement of the Newton-Raphson method,SIAM Rev.,37,,,1995,531,551,,1,,

s2xj12,21,,,,,,Zarzo A.,Ronveaux A.,Godoy E.,Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros.,J. Comput. Appl. Math.,49,,,1993,349,359,,1,,

s2xj13,20,,,,,,Zassenhaus H.,,,über die Fundamentalkonstruktionen der endlichen Körpertheorie,Jahres. Deutscher Math.-Verein.,70,,,1968,177,181,,1,,

s2xj14,19,,,,,,Zeuthen H.G.,,,Sur l'origine de l'Algebre,Danske Vid. Selsk. Mat.-Fys. Medd.,No. 4,,,1919,,,,1,,

s2xj15,3,14,,,,,Zheng S.M.,,,Linear interpolation and parallel iteration for splitting factors of polynomials,J. Computational Mathematics (Beijing),4,,,1986,146,153,,1,,

,5,0,0,0,0,0,Ioakimidis N.I.,,,Determination of poles of sectionally meromorphic functions,J. Comput. Appl. Math.,15,,,1986,323,327,Finds zeros also in some cases; uses argument principle.,1,0,

,5,0,0,0,0,0,Gleyse B.,Kaliaguine V.,,On algebraic computation of number of poles of meromorphic functions in the unit disk, in "Non-linear Numerical Methods and Rational Approximation II", ed. A. Cuyt,,,Kluwer Academic,,1994,241,246,Finds number of zeros in unit disk,1,0,

,19,0,0,0,0,0,Rodet L.,,,Leçons de Calcul d'Aryabhata,Journal Asiatique (Ser. 7),13,,,1879,393,434,Brief mention of quadratic,1,0,

,19,0,0,0,0,0,Busard H.L.L.,,,L'algèbre au Moyen Age: le "liber mensurationum" d'Abu Bekr,Journal des savants,,,,1968,65,124,Arabic treatment of quadratic,1,0,

,19,0,0,0,0,0,Karpinsky L.C.,,,Robert of Chester's latin translation of the algebra of Al-Khowarizmi, in "Contributions to the History of Science",,,Univ. Michigan,Ann Arbor,1930,0,0,Arabic treatment of quadratic,1,0,

,23,0,0,0,0,0,Boys C.V.,,,No title,Nature,23,,,1885,166,167,Uses machine consisting of levers and fulcrums,1,0,

,25,0,0,0,0,0,Mills S.,,,The controversy between Colin MacLaurin and George Campbell over complex roots 1728-1729,Arch. Hist. Exact Science,28,,,1983,149,164,Rule for determining how many roots complex, and bounding them,1,0,

,25,0,0,0,0,0,Weeks D.,,,The Life and Mathematics of George Campbell F.R.S.,Historia Math.,18,,,1991,328,343,Rule for determining how many roots complex, and bounding them,1,0,

,19,0,0,0,0,0,McLaurin C.,,,A second letter to Martin Foulkes concerning the Roots of Aequations with the Demonstration of other Rules in Algebra,Philos. Trans. Roy. Soc. London,36,,,1729,59,96,Gives method of telling if roots are real,1,0,

,20,0,0,0,0,0,Kaltofen E.,Shoup V.,,Subquadratic-Time factoring of Polynomials over Finite Fields, in "Proc. 27th ACM Symp. Theory of Computing",,,,,1995,398,406,Time O(n^1.815),1,0,

,10,0,0,0,0,0,Yun D.Y.Y.,,,Uniform bounds for a class of algebraic mappings,SIAM J. Comput.,8,,,1979,348,356,Deals with GCD's,1,0,

,19,25,29,10,18,2,Lefebure De Fourcy, L.E.,,,Leçons d'Algèbre,,,Gauthier Villars,Paris,1870,0,0,Newton, Secant, Sturm, low-order, square roots, existence,1,0,

,3,0,0,0,0,0,Niell, A.M.,,,The Simultaneous Approximation of Polynomial Roots,Comput. Math. Appl.,41,,,2001,1,14,New proofs of Weierstrass' method, and modified method with improved convergence.,1,0,

,20,0,0,0,0,0,Rademacher, H.,,,Lectures on Elementary Number Theory,,,Blaisdell,New York,1964,0,0,Treats polynomial congruences,1,0,

,20,0,0,0,0,0,Ore, O.,,,Number Theory and its History,,,McGraw-Hill,New York,1948,0,0,Treats polynomial congruences,1,0,

,20,0,0,0,0,0,Riesel, Hans,,,Prime Numbers and Computer Methods for Factorisation,,,Birkhauser,Boston,1985,0,0,Treats quadratic congruences,1,0,

,20,0,0,0,0,0,Uspensky, J.V.,Heaslett, M.A.,,Elementary Number Theory,,,McGraw-Hill,New York,1939,0,0,Treats polynomial congruences,1,0,

,20,0,0,0,0,0,Dickson, L.E.,,,Modern Elementary Theory of Numbers,,,Univ. of Chicago Press,,1938,0,0,Treats quadratic congruences,1,0,

,20,0,0,0,0,0,Ireland, K.,Rosen, M.,,A Classical Introduction to Modern Number Theory,,,Springer-Verlag,New York,1982,0,0,Treats polynomial congruences,1,0,

,20,0,0,0,0,0,Niven, I.,Zuckerman, H.,,An Introduction to the Theory of Numbers,,,J. Wiley,New York,1960,0,0,Treats quadratic congruences;existence of roots,1,0,

,20,0,0,0,0,0,Adams, W.,Goldstein, L.,,Introduction to Number Theory,,,Prentice-Hall,New Jersey,1976,0,0,Treats polynomial congruences,1,0,

,25,0,0,0,0,0,Allenby, R.B.J.T.,,,Rings, Fields and Groups, An Introduction to Abstract Algebra,,,Edward Arnold,London,1983,0,0,Considers solubility by radicals; existence.,1,0,

,20,0,0,0,0,0,Leveque, W.J.,,,Topics in Number Theory,,,Addison-Wesley,Reading, Mass.,1958,0,0,Considers polynomial congruences briefly.,1,0,

,19,0,0,0,0,0,Temple, D.W.,,,Carlyle Circles and the Lemoine Simplicity of Polygon Constructions,Amer. Math. Monthly,98,,,1991,97,108,Geometric method for roots of quadratic,1,0,

,29,0,0,0,0,0,Hunrath, K.,,,Die Berechnung irrationaler Quadratwurzeln,,,Lipsius & Tischer,Kiel,1884,0,0,Detailed treatment of roots, ancient and medieval,1,0,

,19,0,0,0,0,0,Chuquet, N.,,,La Géométrie,,,,Paris,1979,0,0,Geometric treatment of square and cube roots,1,0,

,21,0,0,0,0,0,Lagomasino, G.L.,Cabrera, H.P.,Izquierdo, I.P.,Sobolev Orthogonal polynomials in the complex plane,J. Comp. Appl. Math,127,,,2001,219,230,Treats zeros of certain special polynomials,1,0,

,30,32,0,0,0,0,Ammar, G.S. et al,,,Polynomial Zerofinders based on Szegö polynomials,J. Comp. Appl. Math,127,,,2001,1,16,Applies eigenvalue and continuation methods to equivalent Szego polynomials,1,0,

,19,29,0,0,0,0,King, D.A.,Saliba, G.,,From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kenedy,,,New York Acad. Of Science,New York,1987,0,0,Has articles on quadratics and roots.,1,0,

,21,0,0,0,0,0,Jackson, Bill,,,A Zero-free Interval for Chromatic Polynomials of Graphs,Combinatorics, Prob. And Comput.,2,,,1993,325,336,Shows that P(G,t) has no zeros in [1,32/27]. It is known it has none in (-∞,1),1,0,

,21,3,30,0,0,0,Pasquini, L.,,,On the computation of the zeros of the Bessel polynomials, in "Approximation and Computation", ed R.V.M. Zaher,,,Birkhauser-Verlag,Boston,1994,511,534,Compares simultaneous root-finding with eigenvalue methods, for solutions of 2nd order differential equations.,1,0,

,17,0,0,0,0,0,Sedgewick, R.,,,Algorithms,,,Addison-Wesley,Reading, Mass.,1989,0,0,Considers evaluation,1,0,

,13,29,0,0,0,0,Lam, L.Y.,,,Chu Shih-chieh's "Introduction to mathematical studies",Arch. Hist. Exact Sci.,21,,,1979,1,31,Brief treatment of high order nth roots and equations.,1,0,

,13,29,0,0,0,0,Lam, L.Y.,,,The Chinese connection between the Pascal triangle and the solution of numerical equations of any degree.,Historia Math.,7,,,1980,407,424,Brief treatment of high order nth roots and equations,1,0,

,13,19,0,0,0,0,Libbrecht, U.,,,Chinese mathematics in the thirteenth century, the Shu-shu chiu-chang of Ch'in Chiu-shao,,,MIT Press,Cambridge, Mass.,1973,0,0,Treats a variation of Homer's method,1,0,

,25,0,0,0,0,0,Dickson,,,On the theory of equations in a modular field,Bull. Amer. Math. Soc.,13,,,1906,8,,Deals with Galois resolvents,1,0,

,19,0,0,0,0,0,Tropfke, J.,,,Zur Geschichte d. quadratischen Gleichungen uber dreienhalb Jahrtausende,Jahresber. Deutsch. Math.-Verein,43,,,1933,98,107,Early treatment of quadratic,1,0,

,29,0,0,0,0,0,Saidan, A.,,,The Arithmetic of Al-Uqlidisi,,,D. Reidel,Dordrecht,1978,0,0,Early Arabic treatment of square roots etc.,1,0,

,29,0,0,0,0,0,Tannery, P.,,,L'extraction des racines carrées d'après Nicolas Chuquet,Bibl. Math. Ser. 2,1,,,1887,17,21,Mediaeval treatment of square roots,1,0,

,13,0,0,0,0,0,Blanchard, P.,,,Complex analytic dynamics on the Riemann sphere,Bull. Amer. Math. Soc. (New. Ser.),11,,,1984,85,141,Considers orbits of polynomials,1,0,

,29,0,0,0,0,0,Bryuno, A.D.,,,Continued fraction expansion of algebraic numbers,USSR Comput. Math. and Math. Phys.,4,,,1964,1,15,

Gives expansions of $\frac{1}{\sqrt[3]{2}} etc .$

,1,0,

,29,0,0,0,0,0,Lang, S.,Trotter, H.,,Continued fractions for some algebraic numbers,J. Reine Angew. Math.,255,,,1972,112,134,

Gives continued fractions for some surds such as $\sqrt[3]{2}$ etc.

See p 219-220 also,1,0,

,29,0,0,0,0,0,von Neuman, J.,Tuckerman, B,,Continued fraction expansion of

$\sqrt[3]{2}$

,Math. Tab. Aids Comput.,9,,,1955,23,24,,1,0,

,29,0,0,0,0,0,Richtmyer, R.D.,Devaney, M.,Metropolis, N.,Continued fraction expansions of algebraic numbers,Numer. Math,4,,,1962,68,84,Gives Frequency Distribution of Partial Denominators for Expansion of some surds,1,0,

,13,0,0,0,0,0,Stark, H.M.,,,An explanation of some exotic continued fractions found by Brillhart, in "Computers in Number Theory", eds. A.O.L. Atkin and Birch,,,Academic Press,London,1971,21,35,,1,0,

,13,0,0,0,0,0,Roth, K.F.,,,Rational approximations to algebraic numbers,Mathematika,2,,,1955,1,20,

Shows that, for algebraic numbers α, if |α- $\frac{h}{q} | < \frac{1}{q^{k}} has infinitely many solutions \frac{h}{q}$ , then k=2.

,1,0,

,29,0,0,0,0,0,Rodet, L.,,,Sur une méthode d'approximation des racines carrés, conne dans l'Inde antérieurment à la conquête d'Alexandre,Bull. Soc. Math. France,7,,,1879,98,102,Ancient treatment of square roots,1,0,

,29,0,0,0,0,0,Rodet, L.,,,Sur les méthodes d'approximation chez les anciens,Bull. Soc. Math. France,7,,,1879,159,167,Ancient treatment of square roots,1,0,

,19,0,0,0,0,0,Woepcke, M.,,,Sur un essai de determiner la nature de la racine d'une équation du troisième degré,J. Math. Pure Appl.,19,,,1854,401,406,Refers to Leonardo of Pisa,1,0,

,10,0,0,0,0,0,Adams, W.W.,,,An Introduction to Gröbner Bases,AMS Grad St. in Mathematics,3,,,1991,0,0,Considers greatest common divisors,1,0,

,10,0,0,0,0,0,Apostol, T.M.,,,Resultants of cyclotomic polynomials,Proc. Amer. Math. Soc,24,,,1970,457,463,,1,0,

,19,0,0,0,0,0,Bortollotti, E.,,,La storia della matematica nell'università de Bologna,,,Zanichelli,Bologna,1944,0,0,History of cubic and quadratic,1,0,

,19,0,0,0,0,0,Marie, M.,,,Histoire des sciences mathématiques en Italie Vol. 3,,,Gauthier-Villars,Paris,1841,0,0,Treats cubics,1,0,

,2,7,26,0,0,0,Wang, X.H.,,,On the error estimates for some numerical root-finding methods,Acta Math. Sinica,22,,,1979,638,642,Combined Newton-Secant method; Convergence.,1,0,

,1,2,3,7,12,15,Herzberger, J.,,,Einführung in das wissen-schaftliche Rechnen,,,Addison-Wesley,Bonn,1997,0,0,A good treatment of Bisection, Newton, Secant, Muller, Intervals, Existence. Laguerre, Simultaneous methods,1,0,

,7,0,0,0,0,0,Vogel, K.,,,Die Practica des Algorismus Ratisbonensis,,,,Munich,1954,0,0,Treats Reguli Falsi,1,0,

,29,0,0,0,0,0,Ibn Labban, K.,,,Principles of Hindu Reckoning, transl. M. Levey and M. Petruck,,,Univ. of Wisconson Press,Madison, WI,1965,0,0,Early Arabic treatment of square and cube roots.,1,0,

,11,0,0,0,0,0,Gantmacher, Fr.,,,Theory of Matrices. Vol. 2,,,,Paris,1966,0,0,Treats Routh-Hurwitz criteria etc.,1,0,

,10,0,0,0,0,0,Hermite, C.,,,Remarques sur le théorème de Sturm,C.R. Acad. Sci. Paris,36,,,1853,294,297,,1,0,

,29,0,0,0,0,0,Kern, H. ed,Brill, E.J., ed,,The Aryabhatiya with the commentary Bhatadipika of Paramadicvara (Sanskrit-Text),,,, Neudruck,1972,0,0,,1,0,

,29,0,0,0,0,0,Rangacarya, M., ed.,,,Ganitasarasamgraha,,,,Madras,1912,0,0,,1,0,

,7,0,0,0,0,0,Lefebure De Fourcy, L.E.,,,Leçons d'Algèbre,,,Gauthier-Villars,Paris,1870,0,0,Newton, Secant, Sturm, low-order, square roots, Existence,1,0,

,19,0,0,0,0,0,Karpinski, L.C.,,,The Algebra of Abu Kamil,Bibl. Math. (Ser. 3),12,,,1912,40,55,Early Arabic treatment of quadratic,1,0,

,29,0,0,0,0,0,Drenckhahn, F.,,,Zur Zirkulation des Quadrats und Quadratur des Kreises in den Sulva-Sütras.,Jahres. Deutsch. Math.-Verein,46,,,1936,1,13,Treats early Indian calculation of $\sqrt{2}$ .,1,0,

,19,0,0,0,0,0,Vogel, K.,,,Die Mathematik der Babylonier,,,Vorgr. Mathematik,Hanover, Paderborn,1959,0,0,Babylonians gave formula for quadratic roots.,1,0,

,19,0,0,0,0,0,Rashed, R.,,,Récommencements de l'Algèbre au XI et XII Siècles, in "The Cultural Context of Medieval Learning", ed. J.E. Murdoch,,,Reidel,Dordrecht,1975,33,60,Describes early Arabic treatment of quadratic.,1,0,

,19,0,0,0,0,0,Sesiano, J.,,,Les Méthodes d'analyse indéterminée chez Abu Kamil,Centaurus,21,,,1977,89,105,Describes early Arabic treatment of quadratic.,1,0,

,28,0,0,0,0,0,Anderson B.,,,Polynomial Root Dragging,Amer. Math Monthly,100,,,1993,864,866,Shows how roots of derivative move as real roots of polynomials move.,1,0,

,28,0,0,0,0,0,Gelca R.,,,A Short Proof of a Result on Polynomials,Amer. Math Monthly,100,,,1993,936,937,If f has distinct real roots, so does f'-kf for real k.,1,0,

,28,0,0,0,0,0,Walker P.,,,Separation of the Zeros of Polynomials,Amer. Math Monthly,100,,,1993,272,273,Minimum distance of roots of f'-kf > that of f,1,0,

,18,0,0,0,0,0,Sylvester J.J.,,,On An Elementary proof and generalization of Sir Isaac Newton's hitherto undemonstrated rule for the discovery of imaginary roots,Proc. London Math. Soc.,1,,,1865,1,16,Gives conditions for number of positive (negative) roots,1,0,

,29,0,0,0,0,0,Schönborn,,,Uber die Methode, nach der die alten Griechen (insbesondere Archimedes und Heron),Zeit. Math. Phys,28,,,1883,169,178,Treats square roots among ancient Greeks,1,0,

,19,29,0,0,0,0,Möller,,,Die Mathematik der Sulvasutra,Abh, Math Sem Hamburg Univ.,7,,,1930,173,204,Treats roots of 2 and quadratics in early India,1,0,

,21,0,0,0,0,0,Dimitrov D.K.,,,On a conjecture concerning monotonicity of zeros of ultraspherical polynomials,J. Approx. Theory,85,,,1996,88,97,,1,0,

,21,0,0,0,0,0,Ronveaux A.,Muldoon M.,,Stieltjes sums for zeros of orthogonal polynomials,J. Comput. Appl. Math,57,,,1995,261,269,Considers sums involving zeros of derivatives also.,1,0,

,19,0,0,0,0,0,Khayyam O.,,,A paper of Omar Khayyam transl. A.R. Amir-Moex,Scripta Math.,26,,,1961,323,331,Derives and treats low-degree polynomials,1,0,

,19,0,0,0,0,0,Abu-Kamil,,,Algebra. Tr. & ed M. Levey,,,Univ of Wisconson Press,,1966,0,0,Early treatment of quadratic,1,0,

,19,0,0,0,0,0,de Nemore, J.,,,De Numeris Datis: Transl and ed B.B. Hughes,,,Univ of California Press,,1981,127,132,Treats quadratic,1,0,

,17,0,0,0,0,0,Pan V.Y.,,,Compexity of Computations with Matrices and Polynomials,SIAM Rev.,34,,,1992,225,262,Considers complexity of evaluating polynomials at one or more points.,1,0,

,6,0,0,0,0,0,Pan V.Y.,Reif, J.,,Some Polynomial and Toeplitz Matrix Computations, in "Proc. 28th IEEE Symp Found. Comp. Science",,,,,1987,173,184,Uses Turan's proximity test, Graeffe's method, Winding numbers,1,0,

,2,7,14,0,0,0,Lapidus L.,,,Digital Computation for Chemical Engineers,,,McGraw-Hill,New York,1962,0,0,Good treatment of Newton, Secant, and Bairstow methods,1,0,

,19,0,0,0,0,0,Carra de Vaux B.,,,Penseurs de l'Islam Vol. 2,,,,Paris,1921,0,0,Arabic treatment of a few quadratics,1,0,

,20,0,0,0,0,0,Rademacher H.,,,Lectures on elementary number theory,,,Blaisdell,Waltham, Mass.,1964,0,0,Deals with congruences and cyclotonic polynomials,1,0,

,2,14,26,0,0,0,Fox A.H.,,,Fundamentals of Numerical Analysis,,,The Ronald Press Co.,New York,1963,0,0,Very elementary treatment of Newton, Lin's method and convergence,1,0,

,2,7,0,0,0,0,Harris L.D.,,,Numerical Methods Using Fortran,,,Charles E Merill Bks,Columbus, OH,1964,0,0,Treats secant, inverse quadratic interpolation, and Newton,1,0,

,20,0,0,0,0,0,Davenport H.,,,The Higher Arithmetic,,,Hutchinson & Co. Publish,London,1952,0,0,Deals with congruences,1,0,

,20,0,0,0,0,0,Griffin H.,,,Elementary Theory of Numbers,,,McGraw-Hill,New York,1954,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Jones B.W.,,,The Theory of Numbers,,,Rinehart & Co.,New York,1955,0,0,Deals with Congruences,1,0,

,20,0,0,0,0,0,Stewart B.M.,,,Theory of Numbers,,,MacMillan Co.,New York,1952,0,0,Deals with Congruences,1,0,

,13,0,0,0,0,0,Maclaurin C.,,,The Collected Letters S. Mills ed.,,,Shiva Publishing Ltd,Chesire,1982,0,0,Many letters re polys of degree up to 5th.,1,0,

,10,0,0,0,0,0,Grabiner J.V.,,,Budan de Boislaurent, in Dictionary of Scientific Biography Vol. 2,,,Scribner's,New York,1970,573,574,Tells how many roots between 0 and p>0,1,0,

,25,0,0,0,0,0,Houzel C.,,,La résolution algébrique des équations, in "Sciences á l'époque de la révolution Francaise",,,Blanchard,Paris,1988,17,37,Considers resolution of 5th degree equation and related matters,1,0,

,25,0,0,0,0,0,Humbert P.,,,Les Mathématiques aux XIX Siècle, in "Histoire de la Science", M. Daumas ed.,,,Gallimard,Paris,1957,619,688,,1,0,

,10,0,0,0,0,0,Moigno F.N.W.,,,Note sur la determination du nombre des racine reeles ou imaginaires d'une equation numerique comprises entre des limites donnees,J. Math. Pure Appl.,5,,,1840,75,94,,1,0,

,19,29,0,0,0,0,Midonick H.,,,The Treasury of Mathematics,,,,London,1965,0,0,Quotes early work on surds and quadratics,1,0,

,19,0,0,0,0,0,Archibald R.C.,,,Mathematics before the Greeks,Science (N.S.),71,,,1930,109,121,Babylonian solution of quadratic,1,0,

,19,13,0,0,0,0,Hamburg, R.R.,,,The Theory of Equations in the 18th century:The Work of Joseph Lagrange,Arch. Hist. Exact Sci.,16,,,1976,17,36,Treats quadratic, cubic and uses continured fractions for higher degree in a variation of Horner's method.,1,0,

,25,0,0,0,0,0,Hungerford, T.W.A,,,A Counterexample in Galois Theory,Amer. Math. Monthly,97,,,1990,54,57,,1,0,

,20,0,0,0,0,0,Williams K.S.,,,Polynomials with irreducible factors of specified degree,Canad. Math. Bull,12,,,1969,221,223,,1,0,

,10,20,0,0,0,0,Davenport J.M. et al,,,Computer Algebra: Systems and Algorithms for Algebraic Computation,,,Academic Press,London,1988,0,0,Good treatment of sturm,gcd and polynomials with integral coefficients,1,0,

,18,0,0,0,0,0,Mignotte,,,Some useful bounds, in "Computer Algebra, Symbolic and Algebraic Computation" , Buchberger et al (eds),,,Springer,New York,1982,259,263,Gives bounds on absolute value of roots, and minimal distance between roots,1,0,

,25,19,0,0,0,0,Baumgart, J.E.,,,History of algebra,Hist. Topics for the Math. Classroom,31,,Washington,1969,233,332,Very brief history of low degree equations and existence.,1,0,

,25,0,0,0,0,0,Abel, N.H.,,,Demonstration de l'impossibilite de la resolution algebrique des equations generales qui passent le quatrieme degre, in "Oeuvres completes",Oeuvres completes,1,,,1881,66,94,Proves impossibility of solution by radicals for general equation of degree >4.,1,0,

,25,0,0,0,0,0,Euler, L.,,,Innumerae aequationum formae ex omnibus ordinibus, quarum resolutio exhiberi potest, in "Opera Omnia",Opera Omnia,6,,,0,434,446,Gives many equations of degree > 4 which can be solved by radicals.,1,0,

,25,0,0,0,0,0,Gaal L.,,,Classical Galois Theory with Examples,,,Chelsea,New York,1973,0,0,,1,0,

,21,0,0,0,0,0,Gautschi W.,Kuiijlaars A.B.J.,,Zeros and critical points of Sobolev Orthogonal Polynomials,J. Approx Theory,91,,,1997,117,137,,1,0,

,21,0,0,0,0,0,Lagomasino L.G.,Cabrera H.P.,,Zero location and nth root asymptotics of Sobolev orthogonal polynomials,J. Approx. Theory,99,,,1999,30,43,,1,0,

,21,0,0,0,0,0,Stahl H.,Totik V.,,General Orthogonal Polynomials,,,Cambridge Univ. Press,Cambridge,1992,0,0,Treats zeros of orthogonal polynomials,1,0,

,20,0,0,0,0,0,Glesser Ph,Mignotte M.,,An inequality about irreducible factors of integer polynomials(II),Proceedings of AAECC-8,,,Tokyo,1990,260,266,,1,0,

,10,20,25,0,0,0,Winkler F.,,,Polynomial Algorithmns in Computer Algebra,,,Springer-Verlag,Wien,1996,0,0,Treats GCD,factorization over finite fields and integers,1,0,

,19,0,0,0,0,0,Bortolotti E.,,,L'Algebra nella storia et nella preistoria delle Scienze,Osiris,1,,,1936,184,230,Early treatment of quadratic,1,0,

,13,0,0,0,0,0,Baron M.E.,,,William George Horner,Dict. Sci. Biog.,6,,,1972,510,511,Describes Horner's method,1,0,

,21,0,0,0,0,0,Tutte W.T.,,,Chromials, Hypergraph Seminar, ed C. Berge & D. Ray-Chaudhuri (LNM 411),,,Springer-Verlag,,1974,243,266,Brief mention of zeros,1,0,

,29,0,0,0,0,0,Brent R.P.,,,Fast multi-precision evaluation of elementary functions,J. Assoc. Comput. Mach.,23,,,1976,242,251,Shows that $\sqrt{c}$ can be evaluated, to precision n, in O(M/n) operations. Likewise root of f(x) = 0.,1,0,

,2,13,0,0,0,0,Douady A.,Hubbard J.,,Iteration des polynomes quadratiques complexes,C.R.Acad. Sci. Paris,294,,,1982,123,126,,1,0,

,5,0,0,0,0,0,Ioakimidis N.I.,Anastasselou E.G.,,A modification of the Delves-Lyness method for locating the zeros of analytic functions,J. Comput. Phys.,59,,,1985,490,492,Formula for integrals involved, not using derivatives of function,1,0,

,24,29,0,0,0,0,Cohen A.M.,,,Improving the convergence of alternating series,Internat. J. Comput. Math,9,,,1981,45,53,Applies Aitken acceleration to root finding including $\sqrt{2}$ ,1,0,

,29,0,0,0,0,0,Grant M.A.,,,Approximating square roots and cube roots,Math. Gaz.,66,,,1982,230,230,Gives approximations to square roots of 2,3,5,7,1,0,

,20,0,0,0,0,0,Ljunggren W.,,,On the irreducibility of certain trinomials and quadrinomials,Math Scand,8,,,1960,65,70,Considers irreducibility over the rationals of polynomials of the form xⁿ±x^m±x^p±1,1,0,

,20,0,0,0,0,0,Tverberg H.,,,On the irreducibility of xⁿ±x^m±1,Math. Scand,8,,,1960,121,126,Considers irreducibility over the rationals of polynomials of the stated form,1,0,

,20,0,0,0,0,0,Boyd D.W.,Montgomery H.L.,,Cyclotomic Partitions, in "Number Theory, Banff, AB." Ed R.A. Mullin,,,de Gruyter,Berlin,1990,7,25,Estimates the number of cyclotomic polynomials of degree n and how many have distinct factors,1,0,

,13,19,0,0,0,0,Tweedie C.,,,A Study of the Life and Writings of Colin MacLaurin,Math. Gaz.,8,,,1915,133,151,,1,0,

,19,0,0,0,0,0,MacLaurin C.,,,A Letter from Mr. Colin MacLaurin, Prof of Math at Edin. Etc. concerning equations with impossible roots,Phil. Trans. Roy. Soc. London,34,,,1726,104,112,Gives conditions for roots of low order equations (and general one) to be real,1,0,

,13,0,0,0,0,0,Mills S.,,,The Collected Letters of Colin MacLaurin,,,,Nantwich, Chesire,1982,0,0,,1,0,

,10,0,0,0,0,0,Benis-Sinaceur H.,,,Deux moments dans l'histoire du théorème d'Algèbre de C.F. Sturm,Rev. d'Hist. Sci.,41,,,1988,99,132,Considers original theorem of Sturm and application to logic by Tarski,1,0,

,10,0,0,0,0,0,Darboux G.,,,Note relative au mémoire (de Fourier de 1820), in "Oeuvres de Fourier" Vol. II,,,,,1890,310,314,Refers to Budan's theorem about number of roots in [0,p],1,0,

,10,0,0,0,0,0,Nicholson P.,,,New demonstration of the method invented by Budan and improved by others of extracting the roots of equations,Phil. Mag.,60,,,1822,173,178,Variation on Descartes rule,1,0,

,29,0,0,0,0,0,Chuquet N.,,,Nicholas Chiquet Renaissance Mathematician, Trans. H.G. Flegg et al,,,Reidel,,1985,144,153,Treats roots (surds),1,0,

,0,0,0,0,0,0,Brodie K.W.,,,On Bairstow's method for the solution of polynomial equations,Math. Comp.,29,,,1975,816,826,Bairstow's method is one member of a family. Other members may be better.,1,0,

,6,0,0,0,0,0,Henrici P.,,,Finding zeros of a polynomial by the Q-D algorithm,Comm. Ass. Comp. Mach.,8,,,1965,570,574,Tests on the (slowly convergent) Q-D algorithm, some failures due to equal roots,1,0,

,7,0,0,0,0,0,Miranker W.L.,,,Parallel methods for approximating the root of a function,IBM J Res Dev,13,,,1969,297,301,Uses high order interpolation,1,0,

,7,0,0,0,0,0,Miranker W.L.,,,A survey of parallelism in numerical analysis,SIAM Rev,13,,,1971,524,547,Uses high order interpolation,1,0,

,21,0,0,0,0,0,Varga R.S.,Carpenter A.J.,,Zeros of the partial sums of cos(z) and sin(z). I,Numer. Alg.,25,,,2000,363,375,Considers rates of convergence to associated Szego curves,1,0,

,21,0,0,0,0,0,Driver K.A.,Love A.D.,,Products of hypergeometric functions and the zeros of ₄F₃ polynomials,Numer. Alg.,26,,,2001,1,9,,1,0,

,6,0,0,0,0,0,Kravanja P.,Van Barel M.,,Computing the Zeros of Analytic Functions,,,Springer-Verlag,Berlin,2000,0,0,,1,0,

,13,0,0,0,0,0,Pan V.Y.,,,A New Proximity Test for Polynomial Zeros,Comput. Math. Appl.,41,,,2001,1559,1560,Computes minimum and maximum distance from a fixed point to zeroes.,1,0,

,7,0,0,0,0,0,Wu X.Y.,Xia J.L.,Shao R.,Quadratically convergent multiple roots finding method without derivatives,Comput. Math. Appl,42,,,2001,115,119,Uses formulas involving F(x_n+F(x_n)) where F(x) involves f(x+|f(x)|^1/m) and multiplicity m is assumed known,1,0,

,2,15,0,0,0,0,Gutierrez J.M.,Hernandez M.A.,,An acceleration of Newton's method: Super-Halley method,Appl. Math. Comput.,117,,,2001,223,239,Gives a new third-order method,1,0,

,20,0,0,0,0,0,Stein G.,,,Using the theory of cyclotomy to factor cyclotomic polynomials over finite fields,Math. Comp.,70,,,2001,1237,1251,Takes time about r⁵ for r'th cyclotomic polynomial,1,0,

,15,0,0,0,0,0,Kalantari B.,Park S.,,A computational comparison of the first nine members of a determinantal family of root-finding methods.,J. Comput. Appl. Math.,130,,,2001,197,204,For lower (higher) degree, lower (higher) methods best. Overall most efficient is B₄⁽⁴⁾. Newton is least efficient,1,0,

,3,11,0,0,0,0,Seen F.,Kosmol P.,,A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic,J. Comput. Appl. Math.,130,,,2001,293,307,No comparison with other methods.,1,0,

,21,0,0,0,0,0,Driver K.A.,Love A.D.,,Zeros of ₃F₂ hypergeometric polynomials,J. Comput. Appl. Math.,131,,,2001,243,251,Gives tables of zeros.,1,0,

,13,0,0,0,0,0,Ho P.Y.,,,Yang Hui,Dict. Sci. Biog.,14,,,1976,538,546,Horner's method described,1,0,

,29,0,0,0,0,0,Cody W.J.,Waite W.,,Software manual for the elementary functions,,,Prentice-Hall,Englewood Cliffs N.J,1980,0,0,Gives flow-chart for SQRT program,1,0,

,19,0,0,0,0,0,Hull T.E.,,,The use of controlled precision, in "Proc of IFIP TC2 Working Conference on the Relationship between Numerical Computation and Programming Languages",,,North Holland,Amsterdam,1982,71,84,Gives procedure for solving quadratic,1,0,

,20,0,0,0,0,0,Dimitrov D.K.,,,Connection Coefficients and Zeros of orthogonal polynomials,J. Comput. Appl. Math.,133,,,2001,331,340,,1,0,

,20,0,0,0,0,0,Elbert A.,Laforgia A.,Siafarikas P.,A conjecture on the zeros of ultraspherical polynomials,J. Comput. Appl. Math.,133,,,2001,684,0,,1,0,

,20,0,0,0,0,0,Martinez-Finkelstein A.,,,On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters,J. Comput. Appl. Math.,133,,,2001,477,488,,1,0,

,20,0,0,0,0,0,Grünbaum F.A.,,,Electrostatic interpretation for the zeros of certain polynomials and the Darboux process,J. Comput. Appl. Math.,133,,,2001,397,412,,1,0,

,11,0,0,0,0,0,Liapounoff M.A.,,,Problème générale de la stabilité du mouvement,,,Princeton Univ. Press,,1947,0,0,Considers stability (negative real part of roots).,1,0,

,7,13,0,0,0,0,Swetz F.J.,,,The amazing Chiu Chang Suan Shu,Math. Teacher,65,,,1972,423,430,Mentions Homer and Reguli Falsi in ancient China,1,0,

,13,0,0,0,0,0,Swetz F.J.,,,The evolution of mathematics in ancient China,Math. Magazine,52,,,1979,10,19,Brief mention of Horner's method in early China,1,0,

,29,0,0,0,0,0,Günther S.,,,Die quadratischen Irrationalitaten der Alten und deren Entwickelungsmethoden,Abh. Gesch. Math.,4,,,1882,1,134,Ancient treatment of square roots,1,0,

,19,0,0,0,0,0,Cantor M.,,,I sei cartelli de matematica disfida,Bull. Bibl. Storia Sci. Mat. Fis.,11,,,1878,177,196,Detailed history of cubic,1,0,

,19,0,0,0,0,0,Karpinski,,,The Algebra of Abu Kamil Shoja'ben Aslam,Bibl. Math. Ser. 3,12,,,1912,40,55,Early Arabic treatment of quadratics,1,0,

,19,0,0,0,0,0,Tropfke J.,,,Zur Geschichte d. quadratischen Gleichungen uber dreieinhalb Jahrtausende,Jahresber. Deutsch. Math-Verein.,43,,,1934,98,107,Early treatment of quadratic (see also vol 44 pp 26-47, 95-119),1,0,

,11,0,0,0,0,0,Jury, E.I.,,,On the roots of a real polynomial inside the unit circle and a stability criterion for linear discrete systems.,2nd IFAC congress,,,Basel,1963,142,153,Conditions for roots to be inside the unit circle are given in terms of 2nd order determinants.,1,0,

,11,0,0,0,0,0,Tschauner, J.,,,On the stability of sampled-data systems.,Automat. Remote Control,24,,,1963,831,836,,1,0,

,11,0,0,0,0,0,Desages, A.C..,,,Distance of a Complex Coefficient Stable Polynomial from the Boundary of the Stability Set,Multidim. Systems and Signal Process.,2,,,1991,189,210,The distance from a complex coefficient polynomial to the border of its Hurwitz region is analysed.,1,0,

,11,0,0,0,0,0,Bose, N.K.,Shi, Y.Q.,,A simple general proof of Kharitonov's generalized stability criterion.,IEEE Trans. Circuits and Systems,34,,,1987,1233,1237,Hurwitz property of a set of interval poly's depends on 8 extreme polys.,1,0,

,11,0,0,0,0,0,Petersen, I.R.,,,A class of stability regions for which Kharitonov like theorem holds.,IEEE Trans. Automat. Control.,34,,,1989,1111,1115,Determines if all polynomials in a family have all their roots in a given region.,1,0,

,11,0,0,0,0,0,Bose, N.K.,Kim, K.D.,,Stability of a complex polynomial set with coefficients in a diamond and generalization.,IEEE Trans Circuits and Systems,36,,,1989,1168,1174,Hurwitz property of complex polynomials with coefficients having real & imaginary parts within a diamond depends on 16 edges of the diamonds,1,0,

,11,0,0,0,0,0,Hinrichsen, D.,Pritchard, A.J.,,An application of state space methods to obtain explicit formulae for robustness measure of polynomials, in "Robustness In Identification and Control", ed M. Milanese,,,Plenum,New York,1989,183,206,Studies stability of polynomials under perturbations of the coefficients.,1,0,

,11,0,0,0,0,0,Chapellat, H.,Bhattacharyya, S.P.,Dahleh, M.,On the robust stability of a family of disk polynomials, in "Proc. 29th IEEE Conf. Decision & Control",,,,Tampa,1989,37,42,A set of polynomials with coefficients in disks is Hurwitz stale if the "centre" polynomial is stable, and the norms of a certain two rational functions are < 1.,1,0,

,21,0,0,0,0,0,Varga, R.S.,Carpenter, A.J.,,Zeros of the partial sums of cos(z) and sin(z),Numer. Math,90,,,2001,371,400,Title says it.,1,0,

,29,0,0,0,0,0,Taylor, J.,,,Lilavati,,,,Bombay,1816,0,0,Treats square and cube roots among Hindus,1,0,

,19,29,0,0,0,0,Jouschkewitsch, A.P.,,,Geschichte der Mathematik im Mittelalter,,,,Basel,1964,0,0,Treats roots, low degree world-wide in middle ages.,1,0,

,19,0,0,0,0,0,Franci, R.,Rigatelli, L.T.,,Gianfranco Malfatti e la teoria delle equazioni algebriche, in "Atti del Convegno 'Gianfrancisco Malfatti nella cultura del suo tempo'",,,,Ferraro,1982,179,203,Treats low degree cases.,1,0,

,19,29,0,0,0,0,Juschkewitsch, A.P.,Rosenfeld, B.A.,,Der Mathematik der Lander des Ost. In Mittelalter,,,,Berlin,1963,0,0,Covers square roots, quadratics, and up to quartics.,1,0,

,2,10,0,0,0,0,Tsai, Y.F.,Farouki, R.T.,,Algorithm 812:BPOLY: An object-oriented library of numerical algorithms in Bernstein form,ACM Trans. Math. Softw.,27,,,2001,267,296,Uses Sturm sequences and Newton's method to find real roots of polynomials in Bernstein form. These are more stable than power form, especially for high degree.,1,0,

,21,0,0,0,0,0,Mehta, M.L.,,,Properties of the zeros of a polynomial satisfying a second order linear partial differential equation,Lett. Nuov.Cim.,26,,,1979,361,362,,1,0,

,11,0,0,0,0,0,Kharitonov,,,On the generalization of a stability criterion,Izvest. Akad Nauk Kazakh. SSR. Ser Fiz-Mat,1,,,1978,53,57,,1,0,

,20,0,0,0,0,0,Sun Qui,Han Wenbao,,On absolute trace and primitive roots in finite fields,Chinese J. Contemp. Math (New York),11,,,1990,202,205,,1,0,

,19,0,0,0,0,0,Kropp, G.,,,Vorlesungen uber Geschichte der Mathematik.,,,Biblio. Inst.,Mannheim-Zurich,1969,0,0,History of cubic and quartic.,1,0,

,29,0,0,0,0,0,Boll, M.,,,Histoire des mathematiques.,,,Press. Univ. de France,,1968,0,0,Gives continued fraction for sqrt(2).,1,0,

,25,0,0,0,0,0,Malfatti, G.,,,Dubbj proposti al socio Paolo Ruffini sulla sua dimostrazione della impossibilita di risolvere le equazioni superiori al quarto grado.,Mem Mat. Fis Soc. Ital. Sci.,11,,,1804,579,607,Considers solution by radicals for degree > 4,1,0,

,19,0,0,0,0,0,de Moivre, A.,,,Aequationum quarundam Potestatis tertiae, quintae, septimae, nonae, et superiorum, ad infinitum usque pergendo, in terminis finitis, ad instar Regularum pro Cubicus, quae vocantur Cardani, resolutio analytica.,Phil. Trans. Roy. Soc. London,25,,,1707,2368,0,Describes Cardan's solution of cubic,1,0,

,3,5,0,0,0,0,Ioakimidis, N.I.,Anastesselou, E.G.,,On the simultaneous determination of zeros of analytic or sectionally analytic funtions,Computing,36,,,1986,239,247,Uses integrals to convert to polynomial problem; then uses several simultaneous methods.,1,0,

,5,30,0,0,0,0,Kravanja, P.,Van Barel, M.,Ragos, O. et al.,ZEAL: A mathematical software package for computing zeros of analytic functions,Comput. Phys. Commun.,124,,,2000,212,232,Uses integrals and eigenvalue problems,1,0,

,5,0,0,0,0,0,Kravanja, P.,Cools, R.,Haegermans, A.,Computing zeros of analytic mappings: A logarithmic residue approach.,BIT,38,,,1998,583,596,Uses integrals of logs,1,0,

,2,12,0,0,0,0,Hansen, E.,,,Global optimization using Interval Analysis,,,Marcel Dekker,New York,1992,0,0,Treats Interval Newton method and slope interval Newton method,1,0,

,3,12,0,0,0,0,Petkovic, M.,Herceg, D.,,Methods with corrections for the simultaneous inclusion of polynomial zeros,Nonlinear Analysis,30,,,1997,73,82,Uses interval methods to give bounds on zeros ( obtained simultaneously ).,1,0,

,21,0,0,0,0,0,Buendia, E.,Dehesa, J.S.,Galvez, F.J.,The distribution of zeros of the polynomial eigenfunctions of ordinary differential equations of arbitrary order, in "Orthogonal Plynomials and their Applications", M. Alfaro et al Eds,,,Springer-Verlag,Berlin,1986,222,235,,1,0,

,21,0,0,0,0,0,Zarzo, A.,Dehesa, J.S.,Ronveaux, A.,Newton sum rules of zeros of semi-classical orthogonal polynomials.,J. Comput. Appl. Math.,33,,,1990,85,96,,1,0,

,3,0,0,0,0,0,Bini, D.A.,,,Numerical computation of polynomial zeros by means of Aberth's method.,Numerical Algorithms,13,,,1996,179,200,A very robust and efficient implementation of Aberth's method, never failed on 1000 polynomials of degree up to 25,000. Uses Rouché's theorem for initial guesses.,1,0,

,19,0,0,0,0,0,Dold-Samplonius, Y.,,,The solution of quadratic equations according to al-Samaw'al, in "Mathemata, Festschrift fur Helmuth Gericke",,,Franz Steiner,Stuttgart,1985,95,104,Quadratics among Arabs.,1,0,

,13,29,0,0,0,0,Wang Ling,Needham,,Horner's method in Chinese mathematics: its origins in the root-extraction procedures of the Han dynasty.,T'oung Pao,43,,,1955,345,0,,1,0,

,5,0,0,0,0,0,Anastasselou, E.G.,Ioakimidis, N.I.,,A new approach to the derivation of exact analytical formulae for the zeros of sectionally analytic functions.,J. Math. Anal. Appl.,112,,,1985,104,109,Finds zeros of a related polynomial having integrals for coefficients,1,0,

,3,12,16,0,0,0,Atanassova, L.,,,On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane.,J. Comput. Appl. Math.,50,,,1994,99,107,Uses high-order derivatives and fractional powers of F.,1,0,

,19,0,0,0,0,0,Kennedy, E.S.,,,Studies in the Islamic exact sciences,,,Amer. Univ. Beirut,Beirut,1983,0,0,Quadratics among Arabs,1,0,

,5,12,0,0,0,0,Herlocker, J.,Ely, J.,,An automatic and guaranteed determination of the number of roots of an analytic function interior to a simple closed curve in the complex plane,Reliable Computing,1,,,1995,239,250,Uses interval arithmetic to give bound on integral for number of roots within a curve.,1,0,

,5,0,0,0,0,0,Ioakimidis, N.I.,,,A unified Riemann-Hilbert approach to the analytical determination of zeros of sectionally analytic functions,J. Math. Anal. Appl.,129,,,1988,134,141,Uses integral formulae,1,0,

,17,0,0,0,0,0,Belaga, E.G.,,,On Computing Polynomials in One Variable with Initial Conditioning of the Coefficients,Prob. of Cyber.,5,,,1964,7,15,Describes methods of evaluation more efficient than Horner's; applies to complex numbers.,1,0,

,20,0,0,0,0,0,Dickson, L.E.,,,Introduction to the theory of numbers,,,Univ. of Chicago Press,Chicago,1957,0,0,Treats congruences.,1,0,

,15,0,0,0,0,0,Hernandez. M.A.,Salanova, M.A.,,A Family of Newton type Iterative Processes,Int. J. of Comput. Math.,51,,,1994,205,214,Studies methods such as Halley's involving higher derivatives.,1,0,

,13,0,0,0,0,0,Mellin, H.J.,,,Ein Allgemeiner Satz Über Algebraische Gleichungen,Annales Acad. Scient. Fennicae,7, No.8,,,1915,1,44,Expresses roots in terms of hypergeometric or gamma functions.,1,0,

,21,0,0,0,0,0,Dette, H.,Studden, W.J.,,Some new asymptotic properties of Jacobi, Laguerre, and Hermite polynomials,Constr. Approx.,11,,,1995,227,238,,1,0,

,10,0,0,0,0,0,Sylvester, J.J.,,,On the expressions for the quotients which appear in the application of Sturm's method to the discovery of the real roots of an equation, in "Collected Works",,,,Cambridge,1904,396,398,,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,Note on a remarkable modification of Sturm's theorem, and on a new rule for finding superior and inferior limits to the roots of an equation,Phil. Mag.,6,,,0,14,20,Uses continued fractions,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,On the new rule for finding superior and inferior limits to the real roots of any algebraic equation.,Phil. Mag.,6,,,0,138,140,Uses continued fractions,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,Note on the new rules of limits,Phil. Mag.,6,,,0,210,213,Uses continued fractions,1,0,

,10,0,0,0,0,0,Sylvester, J.J.,,,On the relation of Sturm's auxillary functions to the roots of an algebraic equation, in "Collected Works",,,,Cambridge,1904,59,60,,1,0,

,13,0,0,0,0,0,Ioakimidis, N.I.,,,A note on the closed-form determination of zeros and poles of generalized analytic functions,Stud. Appl. Math.,81,,,1989,265,269,,1,0,

,21,0,0,0,0,0,Faldey, J.,Gawronski, W.,,On the limit distributions of the zeros of Jonquiere polynomials and generalized classical orthogonal polynomials,J. Approx. Theory,81,,,1995,231,249,,1,0,

,21,0,0,0,0,0,Gawronski, W.,,,Strong asymptotics and the asymptotic zero distributions of Laguerre polynomials L_n^(an+α) and Hermite polynomials H_n^(an+α),Analysis,13,,,1993,29,67,Considers limit as n-> ∞,1,0,

,26,0,0,0,0,0,Börsch-Supan, W.,,,Residuenabschätzung Polynom-Nullstellen mittels Lagrange-Interpolation,Numer. Math.,14,,,1970,287,297,Given approximations to zeros, errors are estimated. Applies to multiple roots using high derivatives of p.,1,0,

,21,0,0,0,0,0,van Assche W.,Teugels J.L.,,Second order asymptotic behaviour of zeros of orthogonal polynomials.,Rev. Roumaine Math. Pures Appl.,32,,,1987,15,26,No note.,1,0,

,21,0,0,0,0,0,Elbert A.,Laforgia A.,,New properties of the zeros of a Jacobi polynomial in relation to their centroid.,SIAM J. Math. Anal.,18,,,1987,1563,1572,No note.,1,0,

,2,0,0,0,0,0,Watson W.A.,Philipson T.,Oates P.J.,Numerical Analysis- The Mathematics of Computing.,,,Edward Arnold,London,1969,0,0,Treats Newton.,1,0,

,11,0,0,0,0,0,Katbab A.,Jury E.,,"On the generalization and comparison of two frequency-domain stability robustness results", in Proceedings of the American Cont. Conf.,,,,,1991,1969,1972,Considers stability of perturbed polynomials.,1,0,

,26,0,0,0,0,0,Elzner, L.,,,A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem,Numer. Math.,21,,,1973,425,427,Finds a postieriori bounds on errors for zeros.,1,0,

,15,0,0,0,0,0,Kalantari, B.,,,Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications.,J. Comput. Appl. Math.,126,,,2000,287,318,Uses rational functions involving x and derivatives of f.,1,0,

,29,0,0,0,0,0,Kalantari, B.,Kalantari, I.,,High order iterative methods for approximating square roots.,BIT,36,,,1996,395,399,Generalizes Newton and Halley's methods; uses higher derivatives.,1,0,

,15,0,0,0,0,0,Kalantari, B.,Kalantari, I.,Zaare-Nahandi, R.,A basic family of iteration functions for polynomial root finding and its characterizations,J. Comput. Appl. Math.,80,,,1997,209,226,Uses j'th derivative of p(x) in generalization of Newton's method.,1,0,

,21,0,0,0,0,0,Ismail, M.E.H.,,,An electrostatic model for zeros of general orthogonal polynomials,Pacific J. Math.,193,,,2000,355,369,,1,0,

,20,0,0,0,0,0,Selmer, E.S.,,,On the irreducibility of certain trinomials,Math. Scand.,4,,,1956,287,302,Shows that xⁿ -x-1 is irreducible for all n; xⁿ +x+1 for n ≠ 2 (mod 3) .,1,0,

,21,0,0,0,0,0,Grünbaum, F.A.,,,Variations on a theme of Heine and Stieltjes; An electrostatic interpretation of the zeros of certain polynomials.,J. Comput. Appl. Math.,99,,,1998,189,194,Title says it.,1,0,

,21,0,0,0,0,0,Cheng, S.S.,Lin, Y.Z.,,Detection of positive roots of a polynomial with five parameters,J. Comput. Appl. Math.,137,,,2001,19,48,Special polynomial arising in population dynamics.,1,0,

,20,0,0,0,0,0,Carmichael, R.D.,,,The Theory of Numbers & Diophantine Analyses,,,Dover,New York,1959,0,0,Treats congruences.,1,0,

,4,0,0,0,0,0,Malajovich, G.,Zubelli, J.P.,,On the Geometry of Graeffe Iteration,J. Complexity,17,,,2001,541,573,Describes a stabilized version of Graeffe's method which is almost always globally convergent. Can solve up to degree 1000.,1,0,

,25,0,0,0,0,0,Stubhaug, A.,,,Niels Henrik Abel and His Times…,,,Springer-Verlag,,2000,0,0,Historical treatment for layman.,1,0,

,25,0,0,0,0,0,Von Sohsten de Medeiros,A,,,The fundamental theorem of Algebra Revisited,Amer. Math. Monthly,108,,,2001,759,760,Proof based on Lefschetz Fixed - point theorem,1,0,

,13,19,0,0,0,0,Holm, J.,,,Les Systemes d'équations polynômes dans le Sujuan Juyian (1303),Inst. Hautes Etud. Chinoises,,,,0,0,0,Treats quadratics and higher degree in medieval China,1,0,

,19,29,0,0,0,0,Datta, B.,,,The Science of the Sulba,,,Univ . Calcutta,,1932,0,0,Treats quadratics, surds,1,0,

,10,0,0,0,0,0,Mulders, T.,Storjohann, A.,,The modulo N extended GCD problem for polynomials, in ISSAC '98, ed K.Y. Chwa,,,Springer,,1999,105,112,,1,0,

,10,0,0,0,0,0,Chin, P.,Corless, R.M.,Corliss, G.F.,Optimization strategies for the approximate GCD problem, in ISSAC '98, ed K.Y. Chwa,,,Springer,,1999,228,235,Solves an optimization problem to find coefficients of 'best' GCD when coefficients of the 2 polynomials are known inexactly,1,0,

,13,0,0,0,0,0,Hetz, M.A.,Kaltofen, E.,,Efficient algorithms for computing the nearest polynomial with constrained roots, in ISSAC'98 ed K.Y. Chwa,,,Springer,,1999,236,243,Considers finding minimal perturbation to the coefficients needed to move a root to a point or line etc.,1,0,

,3,0,0,0,0,0,Kirrinnis, P.,,,Fast numerical improvement of factors of polynomials and of partial fractions, in ISSAC'98 ed K.Y. Chwa,,,Springer,,1999,260,267,Uses multidimensional Newton method (Weierstrass),1,0,

,3,0,0,0,0,0,Petkovic, M.S.,Herzeg, D.,,Point estimation of simultaneous methods for solving polynomial equations: a survey,J. Comput. Appl. Math.,136,,,2001,283,307,Conditions for convergence of Durand-Kerner and similar methods depend only on coefficients, degree, and initial approximations to zeros.,1,0,

,12,19,0,0,0,0,Ferreira, J.A.,Patricio, F.,Oliveira, F.,A priori estimates for the zeros of interval polynomials,J. Comput. Appl. Math.,136,,,2001,271,281,Polynomials of degree 2,3,4 with interval coefficients are considered.,1,0,

,21,0,0,0,0,0,Driver, K.,Duren, P.,,Zeros of ultraspherical polynomials and the Hilbert-Klein formulas,J. Comput. Appl. Math.,135,,,2001,293,302,,1,0,

,4,0,0,0,0,0,Rice, T.A.,Siegel, L.J.,,A parallel algorithm for finding the roots of a polynomial, in "Proc 1982 Int. Conf. on Parallel Proc." Ed Batcher,K.E,,,IEEE Comp. Sci. Press,,1982,57,61,Parallel Graeffe's method,1,0,

,19,0,0,0,0,0,Weinberg, J.,,,Die Algebra des Abu Kamil Soga ben Aslam,,,,,1935,0,0,Quadratics among Arabs,1,0,

,13,0,0,0,0,0,Ruffini, P.,,,Sobra la determinazione delle radici nelle equazioni numeriche di qualunque grado, in "Opere Mat. II",,,Cremonese,,1953,281,404,,1,0,

,19,0,0,0,0,0,Giesing, J.,,,Leben und Schriften Leonardos da Pisa,,,Druck von J.W. Thallwitz,Dobeln,1886,0,0,,1,0,

,29,0,0,0,0,0,Thibaut, G.,,,On the Sulvasutras,J. of the Royal Asiatic Soc. Of Bengal,44, part 1,,,1875,252,275,,1,0,

,19,0,0,0,0,0,Lindberg, D.C. (ed),,,Science in the Middle Ages,,,Univ. of Chicago Press,Chicago,1978,0,0,Historical treatment of quadratic,1,0,

,11,0,0,0,0,0,Chen, J.,Fan, M.K.H.,Nett, C.N.,Structured singular values and stability analysis of uncertain polynomials, part 1,Systems Control Lett.,23,,,1994,53,65,Stability with variable coefficients.,1,0,

,11,0,0,0,0,0,Chen, J.,Fan, M.K.H.,Nett, C.N.,Structured singular values and stability analysis of uncertain polynomials, part 2,Systems Control Lett.,23,,,1994,97,109,Stability with variable coefficients.,1,0,

,11,0,0,0,0,0,Joya, K.,Furuta, K.,,Criteria for Schur and D-stability of a family of polynomials constrained with P-norm, in "Proc. IEEE Conf. Dec.and Control",,,,,1991,433,434,Stability of polynomials with constrained coefficients.,1,0,

,11,0,0,0,0,0,Kogan, J.,,,How near is a stable polynomial to an unstable polynomial?,IEEE Trans. Circuits and Systems I,39,,,1992,676,680,Given a stable polynomial, finds how much coefficients can be perturbed and still give stability.,1,0,

,11,0,0,0,0,0,Perez, F.,Abdallah, C.,Docampo, D.,Robustness analysis of polynomials with linearly correlated uncertain coefficients in l^P-normed balls, in "Proc. IEEE Conf. Dec. and Control",,,,,1994,2996,2997,Considers stability of families of polynomials .,1,0,

,11,0,0,0,0,0,Qiu, L.,Davison, E.J.,,A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations,Systems Control Lett.,13,,,1989,413,420,Title says it.,1,0,

,20,0,0,0,0,0,Kraitchik. M.,,,Théorie des nombres, Vol 1,,,Gauthier-Villars et Cie.,Paris,1922,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Kraitchik. M.,,,Théorie des nombres, Vol II,,,Gauthier-Villars et Cie.,Paris,1926,0,0,Treats congruences.,1,0,

,19,0,0,0,0,0,Boyer, C.,,,A History of Mathematics,,,John Wiley & Sons,New York,1968,0,0,Treats history of quadratic and cubic in detail.,1,0,

,19,0,0,0,0,0,Carruccio, E.,,,Mathematics and Logic in History and in Contemporary Thought,,,Faber & Faber,London,1964,0,0,Discusses cubics,1,0,

,19,0,0,0,0,0,Neugebauer, O.,,,Zur Geschichte der babylonischen Mathematik,Quell. Stud. Gesch. Math.,B1,,,1929,78,80,Treats quadratics in Egypt and Babylon,1,0,

,19,0,0,0,0,0,Churchhouse,Muir,,Continued fractions, algebraic numbers, and modular invariants,J. Inst. Math. Appl.,5,,,1969,318,328,Considers continued fraction expansion of root of a cubic,1,0,

,20,0,0,0,0,0,Sierpinski, W.,,,Elementary Theory of Numbers,,,P.W.N.,Warsaw,1964,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Weil, A.,,,Number Theory for Beginners,,,Springer,,1979,0,0,Treats congruences,1,0,

,13,19,25,0,0,0,Smith, D.E.,,,A Source Book in Mathematics,,,McGraw-Hill,New York,1929,0,0,Articles by Cardan, etc on cubic, biquadratic; Abel on quintic; Galois on groups and equations; and Gauss on existence,1,0,

,20,0,0,0,0,0,Wright, H.N.,,,First Course in the Theory of Numbers,,,Wiley,New York,1964,0,0,Considers congruences,1,0,

,10,0,0,0,0,0,Bocher, M.,,,The published and unpublished work of Ch. Sturm on algebraic and differential equations,Bull. Amer. Math. Soc.,18,,,1911,1,18,Historical treatment of Sturm's theorem.,1,0,

,25,0,0,0,0,0,Dieudonné, J.,,,Abrégé d'histoire des mathématiques,,,Hermann,Paris,1978,0,0,Treats existence and solution by radicals,1,0,

,10,20,2,18,0,0,Weisner, L.,,,Theory of Equations,,,Macmillan,New York,1938,0,0,Considers Newton's method, Sturm and related theorems, bounds, rational roots.,1,0,

,19,0,0,0,0,0,Bulmer-Thomas, I.,,,Greek Mathematical Works, 2 vols,,,Harvard Univ. Press,Cambridge, Mass.,1939,0,0,Early Greek treatment of quadratic and cubic.,1,0,

,19,0,0,0,0,0,Jayawardene, S.S.,,,The Trattato d'Albaco of Piero della Francesca, in "Cultural Aspects of the Italian Renaissance…", ed Clough C.H.,,,C. Clough,Manchester,1976,229,243,Treats low-degree equations.,1,0,

,17,0,0,0,0,0,Kiper, A.,,,Parallel Polynomial Evaluation by Decoupling Algorithm,Parallel Algs. Appl.,9,,,1996,145,152,Horner's algorithm of evaluating a polynomial is studied and formulated as a matrix equation Ax=c, with a special bidiagonal A.,1,0,

,21,0,0,0,0,0,Ismail, M.E.H.,Letessier, J.,,Monotonicity of zeros of ultraspherical polynomials, in "Orthgonal Polynomials and Their Applications", Ed. M. Alfaro et al LNM 1329,,,Springer-Verlag,Berlin,1988,329,330,,1,0,

,11,0,0,0,0,0,Soh C.,,,"Frequency domain criteria for robust root location of generalized disc polynomials" in Robustness of Dyns. Sys. with Parameter Uncertainties (M. Mansour, S. Balemi, and W. Truol, eds.),,,Birkhauser,Basel,1992,23,42,Considers stability of perturbed polynomials.,1,0,

,1,2,7,16,0,0,Cheney W.,Kincaid D.,,Numerical Mathematics and Computing (2nd ed.),,,Brooks/Cole Publishing,Monterey, Calif.,1985,0,0,Treats Bisection, Newton, Secant and convergence.,1,0,

,2,7,14,0,0,0,Daniels R.W.,,,An Introduction to Numerical Methods and Optimization Techniques.,,,North-Holland,New York,1978,0,0,Treats Newton, Muller, and Bairstow.,1,0,

,2,14,0,0,0,0,Tompkins C.B.,Wilson, W.L.,,Elementary Numerical Analysis,,,Prentice-Hall, Inc.,New Jersey,1969,0,0,Treats Newton, and Bairstow,1,0,

,2,10,14,17,29,0,Locher, F.,,,Einführung in die Numerische Mathematik,,,,Darmstadt,1978,0,0,Good treatment of Newton, Sturm, Bairstow, Evaluation, and surds,1,0,

,20,0,0,0,0,0,Nagell, T.,,,Sur la recuctibilité des trinomes, in "Attonde Skand. Mat.-Kongr.",,,,,1934,0,0,,1,0,

,13,19,0,0,0,0,Anbouba, A.,,,L'Algèbre al-Badi d'Al-Karaji,,,,Beyrouth,1964,0,0,Treats quadratic and high-order polynomials,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Sur l'insolubilité des équations algébriques …, in "Oeuvres mathematiques de P. Ruffini", Vol. 2,,,,Bologna,1806,107,154,Impossibility of solving polynomials of degree > 4 by radicals,1,0,

,29,0,0,0,0,0,Luckey, P.,,,Die Ausziehung der n.-ten Wurzel und der binomische Lehrsatz in der islamischen Mathematik,Math. Ann.,120,,,1948,217,274,Treats n'th roots by Ruffini-Horner method,1,0,

,21,0,0,0,0,0,Gawronski, W.,Shawyer, B.,,Strong asymptotics and the limit distribution of the zeros of P_n^{(an+α,bn+β)}, in "Progress in Approximation Theory", ed P. Nevai,,,Academic Press,,1991,379,404,,1,0,

,25,0,0,0,0,0,Kolmogoroff, A.N.,Youschkevitch, A.P.,,Les mathématiques au 19^o siècle: Logique Mathématique, Algèbre, Théorie des Nombres, Théorie des Probabilités,,,Nauka,Moscow,1992,0,0,Covers Existence and Solution by Radicals,1,0,

,11,0,0,0,0,0,Fujiwara, M.,,,Über die Algebraischen Gleichungen, deren Wurzeln in einem kreise oder in einer Halbebene liegen,Math. Zeit.,24,,,1926,161,0,Deals with Routh-Hurwitz problem etc.,1,0,

,19,0,0,0,0,0,Toomer, G.I.,,,"Al-Khwärizmi", in Dictionary of Scientific Biography, Vol. 7,,,,,1980,358,365,Arabic solution of quadratic,1,0,

,19,0,0,0,0,0,Al-Tusi (Sharaf Al-Din),,,Oeuvres mathématiques. Algèbre et géométrie au XIIe siècle, ed. R. Rashed,,,,Paris,1986,0,0,Arabic quadratics and cubics,1,0,

,29,0,0,0,0,0,Waterhouse, W.,,,Note on a method of extracting roots in al-Samaw'al,Arch. Hist. Exact Sci.,19,,,1978,383,384,Describes a complicated method for surds which often does not work.,1,0,

,25,0,0,0,0,0,Betti, E.,,,Sulla risoluzione delle equazioni algebriche, in "Opere Mathematiche" Vol 1,,,,,0,31,80,Briefly considers conditions for solubility.,1,0,

,19,0,0,0,0,0,al-Khayyami, Umar,,,The Algebra, transl.D.S. Kasir ( The Algebra of Omar Khayyam),,,,New York,1931,0,0,Treats quadratic and early cubics.,1,0,

,19,0,0,0,0,0,al-Khayyami, Umar,,,The Algebra of Umar Khayyam, transl. H.J.J. Winter, W. Arafat,J. Royal Asiatic Soc. Bengal, Science,16,,,1950,27,70,Treats quadratic and early cubics.,1,0,

,19,0,0,0,0,0,al-Khwarizmi, M.ben Musa,,,The Algebra of Muhammed ben Musa transl. F. Rosen,,,,London,1831,0,0,Arabic quadratics,1,0,

,19,25,0,0,0,0,Tietze H.,,,Famous problems of mathematics Translation of 2nd German ed (1959),,,Graylock Press,Baltimore, Md.,1965,0,0,Actually gives solutions for cubic and quartic and brief treatment of Galois theory.,1,0,

,2,8,0,0,0,0,Voyevodin, V.V.,,,The use of the method of descent in the determination of all the roots of an algebraic polynomial,USSR Comp. Math. Math. Phys.,1 no 2,,,1961,187,195,Uses combination of Newton and method of descent,1,0,

,15,0,0,0,0,0,Hernandez, M.A.,,,An acceleration procedure of Whittaker method by means of convexity,Zbornik Radova fak. Serija matematiku,21,,,1991,27,38,Accelerates Whittaker method ie x_n=1 = x_n-λf(x_n),1,0,

,10,0,0,0,0,0,Sturm, C.,,,a l'occasion de l'article précéedent,J. Math. Pures Appl.,7,,,1842,132,133,,1,0,

,10,0,0,0,0,0,Sturm, C.,,,Demonstration d'un Théorème d'algèbre de M. Sylvester,J. Math. Pures Appl.,7,,,1842,356,368,,1,0,

,16,26,0,0,0,0,Wilkinson, J.H.,,,Practical problems arising in the solution of polynomial equations.,J. Inst. Math. Appl.,8,,,1971,16,35,Considers termination criteria, and error bounds.,1,0,

,11,0,0,0,0,0,Bose, N.K.,,,A simple general proof of Kharitonov's generalized stability criterion,IEEE Trans. Circuits and Systems,34,,,1987,1233,1237,Proves that stability of interval polynomials depends on that of 8 extreme ones.,1,0,

,11,0,0,0,0,0,Ackerman, J.E.,Barmish, B.R.,,Robust Schur stability of a polytope of polynomials,IEEE Trans. Automat. Control,33,,,1988,984,986,,1,0,

,13,0,0,0,0,0,Bortolotti, E.,,,Influenza dell'opera matematica di Paolo Ruffini sullo svolgimento delle teorie algebriche,,,,Modena,1903,0,0,,1,0,

,19,0,0,0,0,0,Saliba, G.,,,The meaning of al-jabr wa'l-muqabalah,Centaurus,17,,,1972,189,204,Vague treatment of quadratic,1,0,

,2,0,0,0,0,0,Goldstein. A.,,,Constructive Real Analysis,,,Harper & Row,,1967,0,0,Advanced treatment of Newton,1,0,

,2,14,16,0,0,0,Noble, B.,,,Numerical Methods,,,Oliver & Boyd,,1966,0,0,Treats Newton, Bairstow, errors,1,0,

,2,7,16,0,0,0,Hammerlin, G.,Hoffmann, K.H.,,Numerical Mathematics, transl. L. Schumacher,,,Springer,,1991,0,0,Treats Newton, Secant and convergence briefly,1,0,

,2,4,7,17,14,11,Zurmuhl, R.,,,Praktische Mathematik für Ingenieure und Physiker,,,Springer,,1963,0,0,Treats Newton, Secant, Graeffe, Bairstow, evaluation, stability, cubic and quartics.,1,0,

,25,0,0,0,0,0,Klein, F.,,,Vorlesungen über die Entwicklung der Mathematik in 19 Jahrhundert. Band I,,,,Berlin,1926,0,0,Some Galois theory,1,0,

,1,2,7,15,0,0,Johnston, R.L.,,,Numerical Methods a Software Approach,,,John Wiley & Sons, Inc.,New York,1982,0,0,Treats Bisection, Newton, Secant, Muller and hybrid methods; Laguerre.,1,0,

,25,0,0,0,0,0,Verriest G.,,,Leçons sur la théorie des équations selon Galois.,,,Gauthier Villars,Paris,1939,0,0,Considers conditions for solubility by radicals.,1,0,

,25,0,0,0,0,0,Verriest G.,,,Oeuvres mathématiques d'E. Galois publiées en 1897, suivies d'une notice sur E.Galois et la théorie des équations algébriques,,,Gauthier Villars,Paris,1951,0,0,Considers conditions for solubility by radicals.,1,0,

,11,0,0,0,0,0,Cieslik J.,,,On possiblities of the extension of Kharitonov's stability test for interval polynomials to the discrete time case.,IEEE Trans. Automat. Control,32,,,1987,237,238,Kharatinov test for interval polynomials does not extend to discrete time case, unless n ≤ 2,1,0,

,11,0,0,0,0,0,Wei K.W.,Yedavalli R.K.,,Invariance of strict Hurwitz property for uncertain polynomials with dependent coefficients.,IEEE Trans. Automat. Control,32,,,1987,907,909,Title says it.,1,0,

,11,0,0,0,0,0,Lipatov A.V.,Sokolov N.I.,,Some sufficient conditions for stability and instability of continuous linear stationary systems.,Autom. Remote Control,39,,,1979,1285,1291,Conditions satisfied by adjacent coefficients of characteristic polynomial,1,0,

,11,0,0,0,0,0,Soh C.B.,Berger C.S.,Dabke K.P.,Addendum to "On the stability properties of polynomials with perturbed coefficients",IEEE Trans. Automat. Control,32,,,1987,239,240,No note.,1,0,

,19,0,0,0,0,0,Lambo Ch. S.J.,,,Une algèbre française de 1484. Nicolas Chuquet,Revue Ques. Scient. (3),2,,,1902,442,472,Treats quadratic.,1,0,

,19,0,0,0,0,0,Bruins E.M.,,,Aperçu sur les mathématiques Babyloniennes,Revue d'Historie des Sciences,3,,,1950,301,314,Babylonians solved quadratic.,1,0,

,19,25,0,0,0,0,Franci R.,Rigatelli L.T.,,Storia della teoria delle equazioni algebriche.,,,,Mursia,1979,0,0,History of low-degree polynomials and existence, solution by radicals.,1,0,

,19,0,0,0,0,0,Vogel K.,,,Bemerkungen zu den quadratischen Gleichungen der babylonischen mathematik.,Osiris,1,,,1936,703,717,Quadratics in Babylonia.,1,0,

,21,0,0,0,0,0,Forrester P.J.,Rogers J.B.,,Electrostatics and the zeros of the classical orthogonal polynomials,SIAM J. Math. Anal.,17,,,1986,461,468,Electrostatic problems solved in terms of zeros of Jacobi polynomials, etc.,1,0,

,19,0,0,0,0,0,Sarton G.,,,A History of Science,,,Harvard Univ. Press,Cambridge, Mass.,1952,0,0,Sumerians solved quadratics and perhaps cubics.,1,0,

,10,0,0,0,0,0,Loria G.,,,Charles Sturm et son oeuvre mathématique,Enseign. Math. Ser. 1,37,,,1938,249,274,Brief treatment of Sturm's Theorem.,1,0,

,13,0,0,0,0,0,Schur J.,,,Zwei Sätze über algebraische Gleichungen mit lauter reelen Wurzeln,J. Reine Angrew. Math.,144,,,1914,75,88,Considers roots of products of 2 polynomials with real roots.,1,0,

,1,2,7,17,0,0,Scraton,,,Basic Numerical Methods: Intoduction to Numerical Mathematics on a Microcomputer,,,,,0,0,0,Treats Bisection, Secant, Newton, and evalutation.,1,0,

,19,0,0,0,0,0,Juschkewitsch A.P.,,,Geschichte der Mathematik im Mittelalter.,,,Teubner,Leipzig,1964,0,0,Touches on quadratic and cubic among Arabs, etc.,1,0,

,2,10,19,25,20,0,Severi F.,,,Lezioni di analisi I,,,Zanichelli,,1933,0,0,Covers Newton, Resultants, low-degree, existence, and rational coefficients.,1,0,

,20,0,0,0,0,0,Lee, T.C.Y.,Vanstone, S.A.,,Subspaces and polynomial factorizations over finite fields,Appl. Alg. Eng. Comm. Comput.,6,,,1995,147,157,No note.,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,Storia della matematica elementare, in "Enciclopedia delle matematiche elementari e complementi", Vol.3 Pt.2,,,,Milan,1950,539,750,Treats quadratic and cubic.,1,0,

,19,0,0,0,0,0,Loria, G.,,,Storia della Matematiche dall'alba della civiltà al secolo XIX,,,,Milano,1950,0,0,Treats quadratic and cubic.,1,0,

,19,0,0,0,0,0,Washington, A.J.,,,Basic Technical Mathematics with Calculus,,,Cummings,Menlo Pk, CA,1970,0,0,A good treatment of quadratic.,1,0,

,25,0,0,0,0,0,Dickson, L.E.,Börger, R.,,The Galois group of a reciprocal quartic equation,Amer. Math Monthly,15,,,1908,85,87,Gives information about solubility by radicals.,1,0,

,25,0,0,0,0,0,Börger, R.,,,On de Moivre's quintic,Amer. Math. Monthly,15,,,1908,171,174,Soluble by radicals,1,0,

,25,0,0,0,0,0,Miller,Blichfeldt,Dickson, L.E.,The points of inflexion of a plane cubic curve.,Ann. Math.,16,,,1914,50,66,Leads to 9th degree equation which is soluble by radicals.,1,0,

,21,0,0,0,0,0,Tricomi, F.G.,,,Sugli zeri dei polinomi sferici ed ultrasferici,Ann. Mat. Pur. Appl.,31,,,1950,93,97,,1,0,

,25,0,0,0,0,0,Bourgne, R.,Azra, J.-P. (eds),,Écris et mémoires mathématiques d'Evariste Galois,,,,,1962,0,0,,1,0,

,19,29,0,0,0,0,Dedron, P.,Itard, J.,,Mathematics and Mathematicians,,,Open Univ Press,Milton Keynes, Eng.,1973,0,0,Treats square roots, quadratics.,1,0,

,25,0,0,0,0,0,Galois, E.,,,Oeuvres mathématique d'Evariste Galois,J. Math. Pures Appl.,11,,,1846,381,444,Includes work on solution by radicals.,1,0,

,19,0,0,0,0,0,Hermite, C.,,,Considerations sur la résolution algébrique de l'équation du cinquème degré.,Nouv. Ann. Math.,1,,,1842,329,336,,1,0,

,13,0,0,0,0,0,Hoe, J.,,,Les Systèmes d'équations polynômes dans le siyuan yujian (1303),.,,Inst. Hautes Etudes Chin.,,0,0,0,Derives several high-order equations & solves by Horner's method.,1,0,

,19,0,0,0,0,0,Ruska, J.,,,Zur altesten arabischen algebre und rechenkust,Sitz.Heidelberger Akad. Wiss. Phil.-Hist Kl.,8 Abt. 2,,,1917,0,0,Arabic quadratics.,1,0,

,1,2,0,0,0,0,Akl, S.G.,,,The Design and Analysis of Parallel Algorithms,,,Prentice-Hall,Englewood Cliffs,1989,0,0,Parallel Bisection and Newton,1,0,

,20,0,0,0,0,0,Adleman, L.M.,Manders, K.,Miller, G.,On taking roots in finite fields, in "Proc. 18th Ann. IEEE Symp. Founds. Comp. Sci.",,,IEEE Comp. Sci. Press,CA, USA,1977,175,178,Treats quadratic residues,1,0,

,13,29,0,0,0,0,Dakhel, A.K.,,,Al-Kashi on Root extraction, ed W.A. Mijab & E.S. Kennedy,,,American Univ.,Beirut,1960,0,0,Describes Ruffini-Horner method of solving polynomials, and Arabic method for surds.,1,0,

,20,0,0,0,0,0,Panario, D.,Viola, A.,,Analysis of Rabin's Poly. Irreducibility test, in "Proc. Latin '98:Theoretical Informatics" ed C.L. Luccesi,,,Springer,,1998,0,0,,1,0,

,19,0,0,0,0,0,Sayili, A.,,,Logical Necessities in Mixed equations by Hamid ibn Turk and the Algebra of his time,,,,Ankara,1962,0,0,Detailed treatment of quadratic among Arabs,1,0,

,19,0,0,0,0,0,Ritter, F.,,,Francois Viéte, inventeur de l'algèbre moderne. Notice sur sa vie et son oeuvre.,,,,Paris,1895,0,0,Treats some low degree equations.,1,0,

,25,0,0,0,0,0,Klein, F.,,,Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert,,,,Berlin,1956,0,0,Brief treatment of fundamental theorem of algebra,1,0,

,21,0,0,0,0,0,Case, K.M.,,,Sum Rules for Zeroes of Polynomials II,J. Math. Phys.,21,,,1980,709,714,Refers to polynomials which satisfy differential equations with polynomial coefficients.,1,0,

,1,2,0,0,0,0,Costabile, F.,Gualtieri, M.I.,Luceri, R.,A New Iterative Method for the Computation of the Solution of Nonlinear Equations,Numer. Alg.,28,,,2001,87,100,Combines bisection & Newton to give a globally convergent method of order 1+ $\sqrt{2}$ ,1,0,

,19,0,0,0,0,0,Kloyda, T.,,,Linear & Quadratic Equations 1550-1650,,,Edwards,Ann Arbor,1938,,,Includes detailed history of quadratic.,1,0,

,2,7,15,24,29,1,Grove, W.E.,,,Brief Numerical Methods,,,Prentice-Hall,Englewood Cliffs,NJ,1966,0,0,Treats bisection, Newton, secant, Muller, Halley,acceleration, square root.,1,0,

,19,0,0,0,0,0,Gullberg, J.,,,Mathematics from the birth of numbers,,,Norton,New York,1997,0,0,Treats low-degree equations in detail, including history.,1,0,

,20,0,0,0,0,0,Dedekind, R.,,,Abriss einer Theorie der höheren Kongruenzen in bezug auf einen reelen Primzahl-Modulus,J. Reine Angew. Math.,54,,,1857,1,26,Treats high-degree congruences,1,0,

,20,0,0,0,0,0,Dedekind, E.,,,Beweis für die Irreduktibilitat der Kreisteilungs-Gleichung,J. Reine Angew. Math,54,,,1857,27,30,Treats high-degree congruences.,1,0,

,11,0,0,0,0,0,Chapellat, H.,Dahleh, M.,Bhattacharyya, S.P.,Robust stability under structured and unstructured perturbations,IEEE Trans. Automat. Contr.,35,,,1990,1100,1108,,1,0,

,11,0,0,0,0,0,Minnichelli, R.J.,Anagnost, J.J.,Desoer, C.A.,An elementary proof of Kharitonov's theorem with extensions.,IEEE Trans. Automat. Control,34,,,1989,995,998,Whole class of polys stable if 4 special ones are. New Proof.,1,0,

,11,0,0,0,0,0,Rantzer, A.,,,Hurwitz testing sets for parallel polytopes of polynomials.,Systems Control Lett.,15,,,1990,99,104,,1,0,

,2,15,0,0,0,0,Palacias, M.,,,Kepler equation and accelerated Newton method.,J. Comput Appl. Math,138,,,2002,335,346,Generalized Newton method. Order 3 version most efficient.,1,0,

,1,5,0,0,0,0,Dellnitz, M.,Schütze, O.,Zheng, Q.,Locating all the zeros of an analytic function in one complex variable,J. Comput. Appl. Math.,138,,,2002,325,333,Adaptive mutli-level algorithm based on argument principle.,1,0,

,19,13,0,0,0,0,Mikami, Y.,,,Scientific Japan, Past & Present, J. Sakurai (ed),,,,,1926,177,198,Brief mention of quadratics etc.,1,0,

,19,29,0,0,0,0,Resnikoff, H.L.,Wells Jr., R.O.,,Mathmatics in Civilization,,,Dover,New York,1984,0,0,Babylonian surds and quadratics,1,0,

,19,0,0,0,0,0,Stillwell, J.,,,Mathematics and its History,,,Springer,New York,1989,0,0,Solution of quadratic and cubic,1,0,

,19,25,0,0,0,0,Dunham, W.,,,Journey through Genius,,,John Wiley & Sons,New York,1990,0,0,Good treatment of cubic, solution by radicals,1,0,

,19,0,0,0,0,0,Hooper, A.,,,The River Mathematics,,,Henry Holt & Co.,New York,1945,0,0,Good treatment of quadratic,1,0,

,25,0,0,0,0,0,Bachmacova, I.,,,Le théorème fondamental de l'Algèbre et la construction des corps algébriques,Archives Internat. D'hist. Des Sciences,13,,,1960,211,222,Detailed history of fundamental theorem of algebra,1,0,

,21,0,0,0,0,0,Laforgia, A,Siafarikas, P.,,Inequalities for the zeros of ultraspherical polynomials, in "Orthogonal Polynomials and Their Applications", ed. C. Brezinski et al,,,Baltzer,Basel,1991,327,330,,1,0,

,21,0,0,0,0,0,Recchioni, M.C.,,,Quadratically convergent method for simultaneously approaching the roots of polynomial solutions of a class of diffferential equations: Applic's to Orthogonal Polynomials,Numer. Alg.,28,,,2001,285,308,,1,0,

,19,0,0,0,0,0,Thompson, J.E.,,,Algebra for the Practical Worker,,,Van Nostrand Reinhold,New York,1982,0,0,Good treatment of quadratic, cubic and quartic.,1,0,

,11,0,0,0,0,0,Petersen, I.R.,,,Extensions to Kharitonov's Theorem, in "Proc. Ist Int. Symp. Sig. Proc. Appls",,,,,0,83,88,,1,0,

,10,4,19,25,0,0,Sansone, G.,Conti, R.,,Lezioni di analisi matematica,,,Cedam,Padova,1958,0,0,Treats Graffe, Sturm. Low degree and existence.,1,0,

,25,0,0,0,0,0,Betti, E.,,,Sulla risoluzione dell'equazione algebriche,Ann. Sci. Mat. Fis,3,,,0,49,115,Treats solution by radicals,1,0,

,17,0,0,0,0,0,Heinrich, H.,,,Einführung in die Praktische Analysis,,,Mayer,Aachen,1963,0,0,Horner's methof for evaluation,1,0,

,19,0,0,0,0,0,Howe, G.,,,Mathematics for the Practical Man,,,Van Nostrand,Princeton,1957,0,0,Simple treatment of quadratic.,1,0,

,20,0,0,0,0,0,Gauss, C.F.,,,Untersuchungen über höhere Arithmetik,,,,Berlin,1889,0,0,Treats congruences.,1,0,

,25,0,0,0,0,0,Gauss, G.F.,,,Die vier Gauss'schen Beweise für die Zerlegung ganzer algebraischer Functionen in reele Factoren ersten oder zweiten Grades (1799-1849),Ostwald's Klassiker,14,,Leipzig,1890,0,0,Proofs of existence,1,0,

,2,4,6,10,25,19,Nicolletti, O.,,,Proprietà generali delle equazioni algebriche,Encycl. Mat. Elementari,1, pt2,Hoepli,Milano,1962,201,322,Covers Newton, Graeffe, Bernouilli, solution by radicals, existence, low-degree.,1,0,

,19,0,0,0,0,0,Togliatti, E.G.,,,Equazioni di secondo, terzo, quarto grado ed altre equazioni algebriche particolari, Sistemi di equazioni algebriche di tipo elementare,Encycl. Mat. Elemtari,,,,1964,265,231,Thorough treatment of low-degree and other special cases.,1,0,

,11,0,0,0,0,0,Barmish, B.R.,,,New tools for robustness analysis, in "Proc. 27th IEEE Conf. Decision Control",,,,,1988,1,6,Surveys applications of Kharitonov's theorem,1,0,

,11,0,0,0,0,0,Fu, M.,Barmish, B.R.,,Maximal unidirectional perturbation bounds for stability of polynomials and matrices.,Systems Control Lett.,11,,,1988,173,179,Bounds perturbations which preserve stability,1,0,

,11,0,0,0,0,0,Tesi, A.,Vicini, A.,,Robustness analysis for uncertain dynamical systems with structured perturbations, in "Proc. IEEE CDC",,,,,1988,519,525,Considers stability of families of polynomials.,1,0,

,19,0,0,0,0,0,Eves H.,,,An Introduction to the History of Mathematics,,,Holt, Rinehart,New York,1969,0,0,Treats history up to quartics,1,0,

,19,0,0,0,0,0,Gandz S.,,,"A Few Notes on Egyptian and Babylonian Mathematics" in Studies and Essays in the History of Science and Learning: Offered in Homage to George Sarton on the Occasion of his Sixtieth Birthday,,,Henry Schumann,New York,1944,449,462,Brief mention of quadratics,1,0,

,11,0,0,0,0,0,Dasgupta S.,,,Kharitonov's theroem revisited,Systems Control Lett.,11,,,1988,381,384,All members of a family are stable if 4 extreme members are,1,0,

,11,0,0,0,0,0,Foo Y.K.,Soh Y.C.,,Stability of a family of polynomials with coefficients bounded in a diamond,IEEE Trans. Automat. Control,AC-36,,,1991,1501,1502,Title says it.,1,0,

,11,0,0,0,0,0,Hinrichson D.,Pritchard A.J.,,Robustness measures for linear systems with applications to stability radii of Hurwitz and Schur polynomials,Internat. J. Control,55,,,1992,809,844,No note.,1,0,

,11,0,0,0,0,0,Hollot C.V.,Kraus F.J.,Tempo R. and Barmish B.R.,Extreme point results for robust stabilization of internal plants with first order compensators,IEEE Trans. Automat. Control,AC-37,,,1992,707,714,Necessary to stabilize only 16 extreme "plants",1,0,

,11,0,0,0,0,0,Hollot C.V.,Yang F.,,Robust stablilization of interval plants using lead or lag compensators,Systems Control Lett.,14,,,1990,9,12,Relies on result on uncertain polynomials,1,0,

,11,0,0,0,0,0,Li Y.,Nagpal K.,Lee E.B.,Stability analysis of polynomials with coefficeints in a disk,IEEE Trans. Automat. Control,37,,,1992,509,513,No note,1,0,

,11,0,0,0,0,0,Panier E.R.,Fan M.K.H.,Tits A.L.,On the robust stability of polynomials with no cross-coupling between the perturbations in the coefficients of even or odd parts.,Systems Control Lett.,12,,,1989,291,299,Stability of a subset guarantees that of a certain family,1,0,

,11,0,0,0,0,0,Pujara L.R.,,,On the stability of uncertain polynomials with dependant coefficients.,IEEE Trans. Automat. Control,AC-35,,,1990,756,759,No note.,1,0,

,11,0,0,0,0,0,Tempo R.,,,A dual result to Kharitonov's theroem.,IEEE Trans. Automat. Control,AC-35,,,1990,195,198,Stability of a family of polynomials depends on four extreme ones.,1,0,

,11,0,0,0,0,0,Tesi A.,Vicino A.,,A new fast algorithm for robust stability analysis of control systems with linearly dependant parametric uncertainites,Systems Control Lett.,13,,,1989,321,329,Considers where coefficients are affine in uncertainty parameters,1,0,

,11,0,0,0,0,0,Tesi A.,Vicino A.,,Robustness anaylsis for linear dynamical systems with linearly correlated parametric uncertainties,IEEE Trans. Automat. Control,AC-35,,,1990,186,191,No note,1,0,

,13,0,0,0,0,0,Barros M. de P.,Lind L.F.,,On the splitting of a complex-coefficient polynomial,Inst. Elec. Eng. Proc. G, Electronic Circuits Syst,133 no.2,,,1986,95,98,Splits into 2 related lower-degree polynomials,1,0,

,11,0,0,0,0,0,Siljak D.D.,,,Parameter space methods for robust control design: a guided tour,IEEE Trans. Automat. Control,AC-34,,,1989,674,688,Considers characteristic equations,1,0,

,11,0,0,0,0,0,Argoun M.B.,,,Frequency domain conditions for the stability of perturbed polynomials,IEEE Trans. Automat. Control,32,,,1987,913,916,Title says it,1,0,

,11,0,0,0,0,0,Barmish B.R.,Tempo R.,Hollot C.V. and Kang H.I.,An extreme point result for robust stability of a diamond of polynomials,IEEE Trans. Automat. Control,AC-37,,,1992,1460,1462,A family of polynomials with real coefficients in a diamond is stable iff 8 extreme polynomials are stable,1,0,

,11,0,0,0,0,0,Chapellat H.,Bhattacharyya S.P.,Dahleh M.,Robust stability of a family of disc polynomials,Internat. J. Control,51,,,1990,1353,1362,No note,1,0,

,11,0,0,0,0,0,Chen J.,Fan M.K.H.,Nett C.N.,"The structured singular value and stability of uncertain polynomials: a missing link", in: Control of Systems with Inexact Dynamic Models eds. Sadegh N. and Chen Y.H.,,,ASME,New York,1991,15,23,No note,1,0,

,13,0,0,0,0,0,Guggenbuhl L.,,,Mathematics in Ancient Egypt: A Checklist (1930-1965),Math. Teacher,58,,,1965,630,634,Contains a partial Bibliography on Egyptian math,1,0,

,19,0,0,0,0,0,King C.,,,Leonardo Fibonacci,Fibonacci Quarterly,1,,,1963,15,17,Leonardo solved a cubic,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,New tools for robustness anaylsis, in "Proc. IEEE CDC",,,,,1988,1,6,Surveys applications of Kharitonov's theorem,1,0,

,20,0,0,0,0,0,Ronyai L.,Szanto A,,Prime-field-complete functions and factoring polynomials over finite fields,Comput. Artif. Intell.,15,,,1996,571,577,No note,1,0,

,20,0,0,0,0,0,Agou, S.,,,Factorisation sur un corps fini k des polynömes à coefficients composé f(x^s) lorsque f(x) est un polynöme irreductible de k[x],C. R. Acad. Sci. Paris,282,,,1976,1067,1068,Finds degrees of divisors of f(x^s),1,0,

,20,0,0,0,0,0,Mertens F.,,,Über die Irreductibilitat der Function x^p-A,Monatsch. Math. Phys.,2,,,1891,291,292,,1,0,

,20,0,0,0,0,0,Kronecker L.,,,Beweis dass für jede Primzahl p die Gleichung 1+x+x²+…+x^n-1=0 irreductibel ist,J. Reine Angew. Math.,29,,,1845,280,0,,1,0,

,11,0,0,0,0,0,Faedo S.,,,Un nuovo problema di stabilita per le equazione algebrich a coefficienti reali,Ann. Scuola Norm. Sup. Pisa. Sci. Fisc. Mat.,(Ser 3) 7,,,1953,53,63,No note,1,0,

,3,0,0,0,0,0,Iliev A.,,,A generalization of Obreshkoff-Ehrlich method for multiple roots of polynomial equations,C.R. Acad. Bulgare Sci. Sci. Math. Nat.,49,,,1996,23,26,Useful if multiplicities known,1,0,

,19,0,0,0,0,0,Notari V.,,,L'equazione di quarto grado,Period. Mat. (Ser. 4),4,,Rome,1924,327,334,Historical treatment of quartic,1,0,

,19,0,0,0,0,0,Karpinski,,,The origin and development of algebra,School Sci. Math,23,,,1923,54,64,Early treatment of quadratic,1,0,

,13,0,0,0,0,0,Pinter A.,,,Zeros of the sum of polynomials,J. Math. Anal. Appl.,270,,,2002,303,305,Gives bound for number of simple and distinct zeros of f+g, where f and g are relatively prime.,1,0,

,21,0,0,0,0,0,Davidson M.,,,On the Farey series and outer zeros of the partition polynomials,J. Math. Anal. Appl.,269,,,2002,431,443,Coeffs all 0 or 1 or -1,1,0,

,11,0,0,0,0,0,Hollot C.V.,Bartlett A.C.,,Some dicrete time counterparts to Kharitonov's stability criteria for uncertain systems,IEEE Trans. Automat. Control,31,,,1985,355,356,,1,0,

,17,0,0,0,0,0,Sedgwick R.,,,Algorithms in C++,,,Addison-Wesley,Reading, MA,1992,0,0,,1,0,

,2,0,0,0,0,0,Ritter I.F.,,,The multiplicity function of an equation (Abstract),Bull. Amer. Math. Soc.,63,,,1957,240,240,Estimate of multiplicity helps convergence of modified Newton's method.,1,0,

,1,2,7,17,10,4,Williams P.W.,,,Numerical Computation,,,Harper & Row, inc.,New York,1972,0,0,Treats Bisection, Newton, Secant, Sturm, Bairstow, QD, Lehmer-Schur, and Graeffe,1,0,

,14,5,6,,,,Williams P.W.,,,Numerical Computation,,,Harper & Row, inc.,New York,1972,0,0,Treats Bisection, Newton, Secant, Sturm, Bairstow, QD, Lehmer-Schur, and Graeffe,1,0,

,10,20,0,0,0,0,Ball R.W.,,,Principles of Abstract Algebra,,,Holt,New York,1963,0,0,Rolle's & Descartes' theorems,1,0,

,19,29,0,0,0,0,Bunt L.N.H.,Jones P.S.,Bedient J.D.,The historical roots of elementary mathematics,,,Prentice-Hall,Englewood Cliffs, NJ,1976,0,0,Early square roots and quadratics,1,0,

,25,0,0,0,0,0,Meschkowski, H.,,,Ways of Thought of Great Mathematicians, Trans. J. Dyer-Bennet,,,Holden-Day,San Francisco,1964,0,0,Gauss' proof of existence,1,0,

,20,0,0,0,0,0,Murty M.R.,,,Prime Numbers and Irreducible Polynomials,Amer. Math. Monthly,109,,,2002,452,458,,1,0,

,25,0,0,0,0,0,Viana P.,Veloso P.M.,,Galois Theory of Reciprocal Polynomials,Amer. Math. Monthly,109,,,2002,466,471,,1,0,

,13,0,0,0,0,0,McNamee J.M.,,,A 2002 update of the supplementary bibliography on polynomials,J. Comput. Appl. Math.,142,,,2002,433,434,,1,0,

,13,0,0,0,0,0,Ruffini, P.,,,Opere Matematiche V 1, 2 ed. E. Bortolotti,,,,Rome,1953,243,406,cf also V2 pp 53-90,1,0,

,27,0,0,0,0,0,Farahmand K.,Flood P.,Hannigan P.,Zeros of a random algebraic polynomial with coefficient means in geometric progression,J. Math. Anal. Appl.,269,,,2002,137,148,,1,0,

,13,0,0,0,0,0,Gergonne J.D.,,,Doutes et réflexions, sur la méthode proposée par M. Wronski, pour la résolution générale des équations algébriques de tous les degrés,Ann. Math. Pures Appl.,3,,,1812,51,59,,1,0,

,19,0,0,0,0,0,Gergonne J.D.,,,Rémarque sur la résolution des équations du quatrième degré par la méthode de M. Wronski,Ann. Math. Pures Appl.,3,,,1812,137,139,,1,0,

,20,0,0,0,0,0,Moenck, R.T.,,,On the efficiency of algorthms for polynomial factoring,Math. Comp.,31,,,1977,235,250,In some cases factors may be found in O(n³+n²logp+nlogp²) steps,1,0,

,11,0,0,0,0,0,Bistritz Y,,,Stability criterion for continous-time system polynomials with uncertain complex coefficients,IEEE Trans. Circuits and Systems,35(4),,,1988,442,448,Restates Kharitonov's criterion,1,0,

,11,0,0,0,0,0,Bose N.K.,Jury E.I.,Zeheb E,On robust Hurwitz and Schur polynomials,IEEE Trans. Automat. Control,33(12),,,1988,1166,1168,,1,0,

,19,0,0,0,0,0,Zeuthen H.G.,,,Geschichte der Mathematik in 16 und 17 Jahrhundert,,,Johnson (reprint),New York,1966,0,0,Treats history of cubic and quartic,1,0,

,19,0,0,0,0,0,Sayili A,,,The Algebra of Ibn Turk,,,,Ankara,1985,0,0,Early treatment of quadratic,1,0,

,19,0,0,0,0,0,MacFarlane A.,,,Théorie de l'équation quadratique,Enseign. Math,2,,,1900,363,369,,1,0,

,19,0,0,0,0,0,Barbarin P,,,Les fonctions hyperboliques dans l'enseignment moyen,Enseign. Math,2,,,1900,443,447,Solves cubic in terms of hyperbolic functions,1,0,

,19,0,0,0,0,0,Casteels L,,,Sur la résolution des équations quadratiques et cubiques, à l'aide des fonctions circulaires et hyperboliques,Enseign. Math,10,,,1908,501,503,,1,0,

,19,0,0,0,0,0,Suchar P,,,Sur le trinôme de second degré,Enseign. Math,17,,,1915,47,52,Conditions that certain numbers lie between roots of a quadratic,1,0,

,25,0,0,0,0,0,Gordan P,,,Ueber den Fundamentalsatz der Algebra,Math. Ann.,10,,,1876,572,572,Existence,1,0,

,19,0,0,0,0,0,Gundelfinger S,,,Bemerkung zur Auflosung der cubischen Gleichungen,Math. Ann.,3,,,1871,272,275,,1,0,

,13,0,0,0,0,0,Abel N.H.,,,Mémoire sur une classe particulière d'équations résolubles algébriquement,Oeuvres,,,,1881,478,507,,1,0,

,11,0,0,0,0,0,Chapellat H,Bhattacharyya S.P.,,An alternative proof of Kharitonov's theorem,IEEE Trans. Automat. Control,34,,,1989,448,450,,1,0,

,19,2,7,0,0,0,Gellert W,Küstner H,Hellwich M et al (eds),The VNR Concise Encyclopedia of Mathematics,,,Van Nostrand Reinhold,New York,1977,0,0,Detailed treatment of low degree equations. Also Newton and Secant.,1,0,

,19,29,0,0,0,0,Hogben L.,,,Mathematics for the Millions,,,W.W. Norton,New York,1993,0,0,Treats square root, quadratic.,1,0,

,11,0,0,0,0,0,Tsypkin Y.Z.,Polyak B,,Frequency domain criteria for l^p-robust stability of continous linear systems,IEEE Trans. Automat. Control,AC-36,,,1991,1464,1469,,1,0,

,20,0,0,0,0,0,Gao S,Panario D,,"Tests and constructions of irreducible polynomials over finite fields" in Foundations of Computational Mathematics, F. Cucker (eds),,,Springer-Verlag,,1997,346,361,,1,0,

,19,0,0,0,0,0,Mahoney M.S.,,,"Mathematics" in Science in the Middle Ages, Lindberg D.C. ed.,,,University of Chicago Pr.,Chicago,1978,145,178,Brief treatment of quadratic among Arabs,1,0,

,19,0,0,0,0,0,Hellman M.J.,,,A unifying technique for the solution of the quadratic, cubic, and quartic,Amer. Math. Monthly,65,,,1959,274,276,Title says it,1,0,

,20,0,0,0,0,0,Ore O,,,Contributions to the theory of finite fields,Trans. Amer. Math. Soc.,36,,,1934,243,274,Higher congruences,1,0,

,20,0,0,0,0,0,Rédei L,Turán P,,Zur Theorie der algebraischen Gleichungen über endlichen Körpern,Acta. Arith.,5,,,1959,223,225,Deals with high degree congruences,1,0,

,11,0,0,0,0,0,Guiver J.P.,Bose N.K.,,Strictly Hurwitz property invariance of quartics under coefficient perturbation,IEEE Trans. Automat. Control,AC-28,,,1983,106,107,,1,0,

,19,0,0,0,0,0,Cayley,,,On a new auxiliary equation in the theory of equations of the fifth order, in "Collected Mathematical Papers" Vol. 4,,,,Cambridge,1891,309,324,,1,0,

,19,29,0,0,0,0,Yan Li,Shiran Du,,Chinese Mathematics- A Concise History (translated by J.N. Crossley and A.W.C. Lun),,,Claredon Press,Oxford,1987,0,0,Treats surds and whether polys have positive roots,1,0,

,19,29,0,0,0,0,Swetz F,Se Ang Tian,,A brief chronological and bibliographic guide to the history of Chinese mathematics,Historia Mathematica,11,,,1984,39,56,Includes brief history of low degree equations in China,1,0,

,13,0,0,0,0,0,Lester D,Chambers S,Lu H.L.,A constructive algorithm for finding the exact roots of polynomials with computable real coefficients,Theor. Comput. Sci.,279,,,2002,51,64,,1,0,

,21,0,0,0,0,0,Boyd D.W.,,,On a problem of Byrnes concerning polynomials with restricted coefficients, II,Math. Comp.,71,,,2002,1205,1217,Coefficients in [1, -1],1,0,

,20,0,0,0,0,0,Kronecker L.,,,Memoire sur les facteurs irreductibles de l'expression xⁿ-1,J. Math. Pures Appl. Ser. 1,19,,,1854,177,0,,1,0,

,19,0,0,0,0,0,Bourbaki N,,,Eléments d'histoire des mathématiques,,,Hermann,Paris,1974,0,0,Treats cubic solution,1,0,

,2,7,10,17,24,6,Isaacson E,Keller H.B.,,Anaylsis of Numerical Methods,,,John Wiley and Sons,New York,1966,0,0,Treats Newton, Secant, Bernoulli, Sturm, Bairstow, evaluation, and acceleration.,1,0,

,19,29,0,0,0,0,Robert of Chester,,,Latin Translation of al-Khwarizmi's Al-Jabr ed. by Barnabus Hughes,,,Stiener Verlag Wiesbaden,Stuttgart,1989,0,0,Treats quadratic and square roots by Arabs,1,0,

,17,0,0,0,0,0,Ceberio M,Granvilliers L.,,Horner's Rule for Interval Evaluation revisited,Computing,69,,,2002,51,81,Interval evaluation improved by 25%,1,0,

,4,10,17,19,0,0,Mineur H,,,Techniques de calcul numérique,,,Dunod,Paris,1966,0,0,Graeffe, Sturm, cubics and quartics evaluation,1,0,

,19,0,0,0,0,0,Tartinville A,,,Théorie des équations et des inéquations du premier et du second degré a une inconnue,,,Nony & Co.,Paris,1902,0,0,Thorough treatment of quadratics,1,0,

,21,0,0,0,0,0,Alvarez-Nodarse R,Dehesa J.S.,,Distribution of zeros of discrete and continuous polynomials from their recurrence relation,Appl. Math. Comput.,128,,,2002,167,190,Treats classical orthogonal polynomial systems,1,0,

,1,2,7,0,0,0,Forsythe G.E.,Malcolm M.A.,Moler C.B.,Computer Methods for Mathematical Computations,,,Prentice-Hall,Englewood Cliffs N.J,1977,0,0,Treats bisection, Newton, Secant,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,Invariance of the strict Hurwitz property for polynomials with perturbations, in "IEEE Conf. On Decision and Control",,,,San Antonio,1983,353,355,Exploits Kharitonov's theorem,1,0,

,11,0,0,0,0,0,Frazer R.A.,Duncan W.J.,,On the criteria for stability for small motions,Proc. Royal Soc.,A-124,,,1929,642,654,Gives conditions for stability,1,0,

,19,0,0,0,0,0,Godt W,,,über den sogennanter irreduzibelen Fall der kubischen Gleischungen,Arch. Math. Phys. (Ser. 3),9,,,1905,213,214,,1,0,

,19,0,0,0,0,0,Jacobi C.G.J.,,,Observatiunculae ad theoriam aequationum pertinentes,J. Reine Ang. Math.,13,,,1835,340,352,Considers degrees up to the sixth,1,0,

,19,0,0,0,0,0,Lodge A,,,On the solution of the general equation of the fourth degree,Quart. J. Math.,19,,,1883,257,262,,1,0,

,10,0,0,0,0,0,Mignosi G,,,Teorema di Sturm e sue estensioni,Rend. Circ. Mat. Palermo,49,,,1925,1,164,,1,0,

,7,0,0,0,0,0,Mammana G.,,,Lemma fondamentale per il calcolo approssimato delle radici di una equazione,Rend. Circ. Mat. Palermo,47,,,1923,109,114,Treats Secant method,1,0,

,7,0,0,0,0,0,Allara E,,,A propisito di una metodo di approssimazione degli zeri di una funzione,Rend. Circ. Mat. Palermo,49,,,1925,387,392,Treats Secant Method,1,0,

,19,0,0,0,0,0,Godman A,Talbert J.F.,,Additional Mathematics- Pure and Applied,,,Longman,London,1971,0,0,Good treatment of quadratic,1,0,

,20,0,0,0,0,0,von zur Gathen J,Gerhard J,,Polynomial factorization over F₂,Math. Comp.,71,,,2002,1677,1698,Works up to degree 250 000,1,0,

,3,0,0,0,0,0,Petkovic M.S.,,,Comments on some recent methods for the simultaneous determination of polynomial zeros,J. Comput. Appl. Math,145,,,2002,519,524,,1,0,

,19,0,0,0,0,0,Staigmüller H,,,Johannes Scheubel, ein deutscher Algebraiker des XVI Jahrhunderts,Abh. Gesch. Math.,9,,,1899,429,469,Considers square roots.,1,0,

,19,0,0,0,0,0,Seidelmann F,,,Die Gesamtheit der kubischen und biquadratischen Gleichungen,Math. Ann.,78,,,1918,230,233,,1,0,

,19,0,0,0,0,0,Kummer E.E.,,,Ueber die cubischen und biquadratischen Gleichungen,Monatsber. Akad. Berlin,,,,1880,930,936,,1,0,

,19,0,0,0,0,0,Réalis S,,,Simples remarques sur les racines entières des équations cubiques,Nouv. Ann. Math. (ser. 2),14,,,1875,289,298,Also pp 424-427,1,0,

,19,0,0,0,0,0,André D,,,Sur l'équation du troisième degré,Nouv. Ann. Math. (Ser. 2),14,,,1875,356,358,,1,0,

,19,0,0,0,0,0,Borden J,,,Question 1229,Analyst,5,,,1878,110,112,,1,0,

,19,25,0,0,0,0,Muir J,,,Of Men and Numbers: The Story of the Great Mathematicians,,,Dodd, Mead,New York,1961,0,0,Cursory treatment of cubic & existence,1,0,

,19,20,25,0,0,0,Haupt O,,,Einführung in die Algebra vol 1,,,,Leipzig,1929,0,0,Treats existence, low degree,1,0,

,20,0,0,0,0,0,Adleman L.M.,Manders K,Miller G,On taking roots in finite fields,Proc. 18th Ann. IEEE Sym. On Found. of Comp. Sci.,,IEEE Computer Soc. Press,California, USA,1977,175,178,Treats quadratic residues,1,0,

,19,0,0,0,0,0,Schuster H.S.,,,Quadratische Gleichungen der Seleukdenzeit aus Uruk,Quel. Stud. Gesch. Math.,B-1,,,1930,194,200,,1,0,

,19,0,0,0,0,0,Starkweather G.P.,,,A solution to the biquadratic by binomial resolvents,Bull. Amer. Math. Soc. (Ser. 2),4,,,1898,524,528,,1,0,

,19,0,0,0,0,0,Dixon T.S.E.,,,A new solution of biquadratic equations,Amer. J. Math.,1,,,1878,283,284,Allegedly easier than classical method,1,0,

,25,0,0,0,0,0,Novy L,,,Origins of Modern Algebra,,,Noordhoff,Groningen,1973,0,0,Treats solubility of equations,1,0,

,25,0,0,0,0,0,Schaaf W.L.,,,Carl Freidrich Gauss,,,Watts,New York,1964,0,0,Popular history of existence theorem,1,0,

,19,0,0,0,0,0,Kummel H,,,To express the roots of the solvable quanitities as symmetrical functions of Homologues,Amer. J. Math.,18,,,1896,74,94,Degrees up to 4th.,1,0,

,19,0,0,0,0,0,Cayley A,,,Note on a cubic equation, in "Collected Math. Papers",,,Cambridge University Prs,Cambridge,1897,421,423,,1,0,

,19,0,0,0,0,0,Pleskot A,,,Nouveau procédé pour résoudre les équations du trosieme degré,Nouv. Ann. Math.Ser. 3,18,,,1899,65,66,,1,0,

,19,0,0,0,0,0,McClintock E,,,A simplified solution of the cubic,Ann. Math. Ser. 2,2,,,1901,151,152,,1,0,

,19,0,0,0,0,0,Procissi A,,,Il caso irriducibile della equazione cubica da Cardano,Period. Mat. Ser. 4,29,,,1951,263,280,Thorough historical treatment of cubic,1,0,

,19,0,0,0,0,0,Valeriani V,,,Suluzione analitice delle equazioni biquadratiche complete,Giorn. Mat.,13,,,1875,99,106,Solves quartic,1,0,

,13,0,0,0,0,0,Antomari X,,,Sur les conditions qui expriment qu'une équation de degré m n'a que p racines destinct,Nouv. Ann. Math.Ser 3,16,,,1897,63,75,,1,0,

,19,0,0,0,0,0,Fontené G,,,Discussion des équations de degrés 2,3,4,5 au point de vue des racines multiples,Nouv. Ann. Math.Ser. 4,11,,,1911,340,355,Multiple roots of low-degree,1,0,

,19,0,0,0,0,0,Janni V,,,Supra una formola di Arnhold,Giorn. Mat.,21,,,1883,213,216,Treats quartic,1,0,

,28,0,0,0,0,0,Rados G,,,Sur la théorie des racines de l'unité,Rend. Circ. Mat. Palermo,36,,,1913,299,304,,1,0,

,21,0,0,0,0,0,Cipolla M.,,,Sulle equazioni algebriche le cui radici sono tutte radici dell' unita,Rend. Circ. Mat.Palermo,38,,,1914,370,375,,1,0,

,20,0,0,0,0,0,Dora D.J. (ed),Fitch J (ed),,Computer Algebra and Parallelism,,,Academic Press,San Diego, CA,1989,133,141,Treats factorization over integers,1,0,

,1,2,7,17,10,0,King J.T.,,,Introduction to Numerical Computation,,,McGraw Hill,New York,1984,0,0,Treats bisection, Newton, Secant, evaluation, and Descartes' rule.,1,0,

,29,0,0,0,0,0,Phillips G.M.,Taylor P.J.,,Computers,,,Methuen,London,1969,0,0,Treats bisection and Newton's method as applied to square roots.,1,0,

,11,0,0,0,0,0,Milanese M et al (eds),,,Proc. Intern. Workshop on Robustness in Identification and Control p.95, 123, 144, 181,,,Plenum,New York,1989,0,0,Several papers on stability of polynomials with perturbed coefficients,1,0,

,5,0,0,0,0,0,Kravanja P,van Barel M,,Computing the Zeros of Analytic Functions,,,Springer-Verlag,Berlin,2000,0,0,Mostly integration methods,1,0,

,15,0,0,0,0,0,Abramchuk V.S.,Lyashko S.I.,,Solution of equations with one variable,J. Math. Science,109,,,2002,1669,1679,Generalizes Secant method,1,0,

,21,0,0,0,0,0,de Bruin M.G.,Groenevelt W.G.M.,Meyer H.G.,Zeros of Sobolev orthogonal polynomials of Hermite type.,Appl. Math. Comput.,132,,,2002,135,166,,1,0,

,20,0,0,0,0,0,Moore P.M.A.,Norman A.C.,,Implementing a polynomial factorization and GCD package, in "Proc. Of 1981 ACM Symp. On Sym. Alg. Comp.",,,,,1981,109,116,,1,0,

,20,0,0,0,0,0,Fleischmann P.,Holder M. Chr.,,The black-box Niederreiter algorithm and its implementation over the binary field,Math. Comp.,72,,,2003,1887,1899,Factorization of high-degree polynomials over binary field. Includes parallel program.,1,0,

,20,0,0,0,0,0,Wang P.S.,,,Symbolic Computation and Parallel Software, in "Parallel Computation", ed. H.P. Zima,,,,,1991,316,337,Treats factorization over integers,1,0,

,2,10,19,25,0,0,Archibald R.C.,,,Outline of the History of Mathematics (no.2 of the Herbert Ellsworth Slaught Memorial Papers),Amer. Math. Monthly,56, No.1 Pt.2,,,1949,1,114,Historical treatment of low degree, Newton, Sturm, existence, etc.,1,0,

,19,0,0,0,0,0,Pellet A.E.,,,Sur l'équation du quatrième degré et les fonctions elliptiques.,Bull. Soc. Math. France,14,,,1886,90,93,,1,0,

,19,0,0,0,0,0,Darbi G,,,Sulle equazioni di 4e Grado,Giorn. Math.,38,,,1990,153,164,Treats quartic,1,0,

,19,0,0,0,0,0,Briot F,,,Résolution de l'équation du quatrième degré,Nouv. Ann. Math. Ser. 2,20,,,1881,225,227,Solves quartic,1,0,

,19,0,0,0,0,0,Perrin R,,,Sur une nouvelle méthode de résolution de l'équation du quatrième degré, et son application á quelques équations de degrés superieurs,Bull. Soc. Math. France,10,,,1882,139,146,Solves quartic and some higher order equations,1,0,

,19,0,0,0,0,0,Lucas F,,,Nature des racines de l'équations du quatrième degré,Bull. Soc. Math France,18,,,1890,145,149,Considers quartic,1,0,

,25,0,0,0,0,0,Abel N.H.,,,Mémoire sur les équations algébriques, ou l'on démontre l'impossibilité de la résolution de l'équation généal du cinquième degré,Oeuvres complete,1,,,1824,28,33,Impossibility of solution by radicals for degrees >4,1,0,

,25,0,0,0,0,0,Abel N.H.,,,Démonstration de l'impossibilité de la résolution algébrique des équation générales qui passent le quatrième degré,Oeuvres complete,1,,,1826,66,87,Impossibility of solution by radicals for degrees >4,1,0,

,21,0,0,0,0,0,Abel N.H.,,,Abhandlung über eine besondere Klasse algebraisch auflösbarer Gleichungen,Ostwald's Klassiker,111,,Leipzig,1900,1,50,Deals with xⁿ-1=0,1,0,

,11,10,19,25,2,7,Aleksandrov A.D. et al,,,Mathematics: Its Content, Methods, and Meaning. 3 vols.,,,MIT Press,Cambridge, Mass.,1965,0,0,Brief treatment of low-degree, existence, Sturm, Hurwitz, Newton, Secant, and Graeffe's methods.,1,0,

,11,0,0,0,0,0,Aleksandrov A.D.,Nikolaev Yu.P.,,The subspace of asymptotical stability of a class of linear stationary systems,Autom. Remote Control,35,,,1974,521,528,,1,0,

,2,7,17,0,0,0,Ketter R.L.,Prawel S.P. jr.,,Modern Methods of Engineering Computation,,,McGraw-Hill Book Co.,New York,1969,0,0,Treats Newton, reguli falsi, evaluation,1,0,

,1,2,7,19,14,16,LaFara R.L.,,,Computer Methods for Science and Engineering,,,Hayden Book Co.,Rochelle Park, N.J.,1973,0,0,Treats bisection, Newton, Secant, Lin, convergence, and low degree.,1,0,

,19,0,0,0,0,0,Levi H,,,Elements of Algebra,,,Chelsea,New York,1962,0,0,Simple treatment of quadratic.,1,0,

,19,0,0,0,0,0,Lumpkin B,,,A mathematics club project from Omar Khayyam,Math. Teacher,71,,,1978,740,744,Geometric solution of cubic,1,0,

,22,0,0,0,0,0,Rouillier F,Zimmermann P,,"Efficient isolation of polymonials' real roots",J. Comput. Appl. Math.,162,,,2004,33,50,Uses Vincent-Akritas method with multiple-precision interval arithmetic. Works up to degree 1000 or more.,1,0,

,19,0,0,0,0,0,Berggren L. J.,,,Innovation and tradition in Sharaf al-Din al-Tusi's al Mu'adalat,Journal of the American Oriental Society,110,,,1990,304,309,Treats conditions for existence of roots of cubic, etc.,1,0,

,19,0,0,0,0,0,Hogendijk J.P.,,,Sharaf al-Din al-Tusi on the number of positive roots of cubic equations,Historia Mathematica,16,,,1989,69,85,Uses geometric methods to find roots of cubic,1,0,

,19,0,0,0,0,0,Rashed R,,,Sharaf al-Din al-Tusi, oeuvres mathématiques: Algèbre et géométrie au XII siècle,,,S.E.B.L.,Paris,1986,0,0,Adhoc method for cubic,1,0,

,19,0,0,0,0,0,King D.A. (ed),Kennedy M.H. (ed),,Studies in the Islamic Exact Sciences,,,Amer. Univ Of Beirut Pr.,Beirut,1983,0,0,Brief treatment of quadratic and cubic by Arabs,1,0,

,19,0,0,0,0,0,Hoyrup J,,,The formation of 'Islamic Mathematics': sources and conditions,Science in Context,1,,,1987,281,329,Historical/philosophical discussion of early solution of quadratic,1,0,

,11,0,0,0,0,0,Ghosh B.K.,,,Some new results on the simultaneous stabilizability of a family of single input, single output systems,Systems Control Letters,6,,,1985,39,45,,1,0,

,11,0,0,0,0,0,Yeung K.S.,,,Linear system stability under parameter uncertainties,Internat. J. Control,38-2,,,1983,459,464,,1,0,

,11,0,0,0,0,0,Lin H,Hollot C.V.,Bartlett A.C.,Stability of families of polynomials: geometric considerations in coefficient space.,Internat. J. Control,45,,,1987,649,660,,1,0,

,4,,,,,,Aleksandrov A.D. et al,,,Mathematics: Its Content, Methods, and Meaning. 3 vols.,,,MIT Press,Cambridge, Mass.,1965,0,0,Brief treatment of low-degree, existence, Sturm, Hurwitz, Newton, Secant, and Graeffe's methods.,1,0,

,14,,,,,,Isaacson E,Keller H.B.,,Anaylsis of Numerical Methods,,,John Wiley and Sons,New York,1966,0,0,Treats Newton, Secant, Bernoulli, Sturm, Bairstow, evaluation, and acceleration.,1,0,

,21,0,0,0,0,0,Méray C.,,,Démonstration analytique … des racines des équations binomes,Ann. Ecole Norm Ser. 3,2,,,1885,337,356,Roots of xⁿ = a,1,0,

,19,0,0,0,0,0,Becker O.,,,Grundlagen der Mathematik in geschichtlicher Entwicklung,,,Alber,Freiburg,1954,0,0,Babylonian treatment of quadratic,1,0,

,2,4,6,0,0,0,Nicoletti O.,,,Proprieta generali delle Equazioni Algebriche: IV: Metodi di approssimazione, in "Enciclopedia delle Mat.", ed Berzolari L et al,,1 Pt 2,Hoepli,Milano,1932,236,248,Treats Newton, Graeffe, Bernoulli,1,0,

,19,0,0,0,0,0,Am Ende H,,,Ueber eine die gleichungen zweiten, dritten und vierten grades umfessande auflösungsmethode,Arch. Math. Phys. Ser. 2,3,,,1885,103,106,Treats degree 2-4,1,0,

,19,0,0,0,0,0,Archibald R.C.,,,Notes on Omar Khayyam (1050-1122),Pi mu Epsilon Journal,1,,,1953,351,358,Very brief discussion of cubics according to Arabs.,1,0,

,19,0,0,0,0,0,Amighi G.,,,Note di algebra di Pierro della Francesa,Physis,11,,,1967,421,424,Treats low degrees.,1,0,

,19,0,0,0,0,0,Artom,,,Le equazioni di secondo grado presso I Greci,Period. Mat. Ser. 4,2,,,1922,326,342,History of quadratic among Greeks.,1,0,

,11,0,0,0,0,0,Bartlett A.C.,,,Root locations of an entire polytope of polynomials: it suffices to check the edges,Math. Of Control, Signals, and Systems,1,,,1988,61,71,,1,0,

,10,0,0,0,0,0,Björling C.F.E.,,,Sur la réalité des Racines d'équations algébriques.,Arch. Math. Phys.,48,,,1868,363,375,,1,0,

,19,0,0,0,0,0,Candido G.,,,La risoluzioni della equazione di quarto grado,Period. Mat. Ser. 4,21,,,1942,21,44,History of quartic,1,0,

,19,0,0,0,0,0,Candido G.,,,Le risoluzioni della equazione di quarto grado: fagnano,Period. Mat. Ser. 4,21,,,1942,151,176,Treats quartic and lower degree.,1,0,

,19,0,0,0,0,0,Candido G.,,,La risoluzioni della equazione di quarto grado: Ferrari-Eulero-Lagrange.,Period. Mat. Ser. 4,21,,,1942,88,106,History of solution of quartic,1,0,

,19,0,0,0,0,0,Carnahan W.H.,,,Geometric solutions of quadratic equations,School Sci. Math.,47,,,1947,689,690,Greek and Arabic solutions,1,0,

,19,0,0,0,0,0,Cassina,,,Sulla equazioni cubiche di Al-Biruni,Period. Mat. Ser. 4,21,,,1942,3,20,Arabic treatment of cubic,1,0,

,19,0,0,0,0,0,Carnahan W.H.,,,History of Algebra,School Sci. Math.,46,,,1946,7,12,Note: also pages 125-130. Simple history of Cardan's solution of cubic.,1,0,

,19,23,0,0,0,0,Citterio G.C.,,,Un regolo per la lettura immediata delle radici di un'equazione cubica trinoma,Period. Mat. Ser. 4,41,,,1963,272,278,A mechanical device for solving cubics,1,0,

,19,0,0,0,0,0,De Pasquale L.,,,Le equazioni di terzo grado in "quesiti et inventioni diverse di Tartaglia",Period. Mat. Ser. 4,35,,,1957,79,93,History of solution of cubic,1,0,

,13,0,0,0,0,0,Fischer F.W.,,,Einiges über Gleichungen, welche auf reciproke Gleichungen zurrückgeführt werden können,Arch. Math. Phys.,55,,,1873,294,301,,1,0,

,19,0,0,0,0,0,Franci R,,,Towards a history of algebra from Leonardo of Pisa to Luca Pacioli,Janus,72,,,1985,17,82,History of low-degree polynomials in the Middle Ages.,1,0,

,13,0,0,0,0,0,Galois E,,,Note sur la résolution des équations numériques,Bull. Univ. Sci.Indust. Sec.1,Bull. Sci.Math.Astr.,13,,,1830,413,414,,1,0,

,19,0,0,0,0,0,Gergonne M,,,Remarque sur la résolution des équations du quartième degré par la méthode de M. Wronski,Ann. Math. Pures. Appl.,3,,,1812,137,139,,1,0,

,19,0,0,0,0,0,Grassman H,,,Elementare Auflösung der allgemeinen Gleichung vierten Grades.,Arch. Math. Phys.,51,,,1870,93,96,Treats quartic,1,0,

,19,0,0,0,0,0,Grunert J.A.,,,Die allgemeine Cardanische Formel,Arch. Math. Phys.,40,,,1863,246,249,Treats Cardan's formula for cubic.,1,0,

,19,0,0,0,0,0,Hoppe R,,,Ueber transformation und numerische Lösung der kubisehen Gleichung,Arch. Math. Phys. Ser.2,13,,,1894,95,99,Treats cubic,1,0,

,19,0,0,0,0,0,Hoppe R,,,Bezirke der drei wurzelformen der Gleichung 4: grades,Arch. Math. Phys. Ser.2,14,,,1896,398,404,Treats quartic,1,0,

,19,0,0,0,0,0,Karpinski L.C.,,,The mathematics of the Orient,School. Sci. Math.,34,,,1934,467,472,Brief treatment of ancient quadratics,1,0,

,19,0,0,0,0,0,Liebrecht E,,,Ueber kubische Gleichungen,Arch. Math. Phys.,59,,,1876,217,217,Brief note about cubic,1,0,

,19,0,0,0,0,0,Liebrecht E,,,Ueber rationale Wurzeln kubischer Gleichungen in rationaler Gestalt,Arch. Math. Phys.,60,,,1877,216,218,Treats cubic,1,0,

,29,0,0,0,0,0,Gurjar L.V.,,,The value of the $\sqrt{2}$ given in the Sulvasutras,J. Univ. Bombay N.S.,10 (5),,,1942,6,10,Early calculation of sqrt (2),1,0,

,19,0,0,0,0,0,Ligowski W,,,Bermerkungen zu der in Tell 55. Seite 426 gegebenen Auflösung der Gleichungen vierten Grades.,Arch. Math. Phys.,67,,,1863,446,447,Treats quartic,1,0,

,19,0,0,0,0,0,Ligowski W,,,Zuruckfuhrung der vollstundigen Gleichung vierten Grades auf eine reciproke Gleichung zweiten Grades,Arch. Math. Phys.,65,,,1880,426,429,Studies quartics via a reciprocal quadratic.,1,0,

,19,0,0,0,0,0,Luckey P,,,Thabit ibn Qurra uber den geometrischen Richtigkeitsnachweis der auflosung der quadratischen Gleichungen,Ber. Verhand. Sach. Akad. Wiss. Leipzig Math-Phys,93,,,1941,93,114,Geometric solution of quadratic by Arabs,1,0,

,19,0,0,0,0,0,Milarch E,,,Die kubische Gleichungen,Unter. Math. Natur.,14,,,1908,30,30,Brief treatment of cubic,1,0,

,19,0,0,0,0,0,Eckhardt E.,,,Zur Auflösung der Gleichung vierten Grades,Zeit. Math. Naturwiss. Unterr.,41,,,1910,33,34,Treats quartics,1,0,

,21,0,0,0,0,0,Kim et al,,,Sobolev-type orthogonal polynomials and their zeros,Rend. Mat. Ser. 7,17,,,1997,423,444,,1,0,

,19,29,0,0,0,0,Milhaud G.,,,La géometrie d'Apastamba,Rev. Gen. Sci. Pures Appl.,21,,,1910,512,520,sqrt(2) and quadratic in early India,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Marginal notes on Cajori's History of Mathematics,School Sci. Math.,19,,,1919,830,835,Brief Reference to cubics,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Marginal notes on Cajori's History of Mathematics,School Sci. Math.,23,,,1923,138,149,Slight reference to low-degree and solution by radicals,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Historical note on the solution of equations,School Sci. Math.,24,,,1924,509,510,Shows that solution of cubic not completed until mid-18th century,1,0,

,19,0,0,0,0,0,Natucci A.,,,Storia della teoria delle equazioni I. Dall'antichita all'inizio del secolo XVI^o,Period. Mat. Ser. 4,41,,,1963,257,271,Ancient quadratics,1,0,

,19,0,0,0,0,0,Nell A.M.,,,Ueber die allgemeine Auflösung der Gleichungen vierten Grades,Arch. Math. Phys.,56,,,1874,407,421,Treats quartics,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Trickovic S.,Herceg D.,On Euler-like Methods for the Simultaneous Approximation of Polynomial Zeros,Japan J. Ind. Appl. Math.,15,,,1998,295,315,Describes a fourth-order simultaneous method, combining float and inclusion methods,1,0,

,19,25,0,0,0,0,Reves G.E.,,,Outline of the History of Algebra,School Sci. Math.,52,,,1952,63,69,Brief treatment of low degree, and existence,1,0,

,19,0,0,0,0,0,Rodet L.,,,L'Algèbre d'Al-Kharizmi,J. Asiatique Ser. 7,11,,,1878,5,98,Arabic treatment of quadratic,1,0,

,19,0,0,0,0,0,Sommer J.,,,Eine Lösung der Gleichungen vom dritten und vierten Grade vermittelst desselben Princips,Arch. Math. Phys.,27,,,1856,354,358,Treats cubic and quartic,1,0,

,13,0,0,0,0,0,Shönemann T.,,,Ueber die Beziehungen, welche zwischen den Wurzeln irreductibiler Gleichungen…,Denk. Kais. Akad. Wiss., Math.-Nat…,5,,,1853,143,156,,1,0,

,19,0,0,0,0,0,Thureau-Dangin F.,,,Notes Assyriologiques,Rev. Assyr. Archeol. Orient.,29,,,1933,136,142,Ancient treatment of quadratic,1,0,

,25,0,0,0,0,0,Vitali G.,,,Sul teorema fondamentale dell'algebra,Period. Mat. Ser. 4,8,,,1928,102,105,Treats existence,1,0,

,19,0,0,0,0,0,Vogel K.,,,Babylonische Mathematik,Bayer. Blatt. Gymn.-Schul.,71,,,1935,27,29,Ancient quadratics,1,0,

,19,0,0,0,0,0,Weltzien C.,,,Die rationale Lösung der Gleichung dritten Grades,Arch. Math. Phys. Ser. 3,28,,,1919,91,92,Brief note on cubics,1,0,

,19,0,0,0,0,0,Weltzien C.,,,Sopra una speciale classe di equazioni di terzo grado,Period. Mat. Ser. 3,9,,,1911,174,179,Treats special case of cubic,1,0,

,19,0,0,0,0,0,Thureau-Dangin F.,,,Notes Assyriologiques,Rev. Assyr. Archeol. Orient.,30,,,1933,184,188,Ancient quadratic,1,0,

,20,0,0,0,0,0,Ore O.,,,ueber die Reduzibilitat von algebraischen Gleichungen,Vid. Skrift. Math.-Nat. Kl.,??,,,1923,1,37,,1,0,

,11,0,0,0,0,0,Tsypkin Y.,Polyak B.,,Frequency criteria of linear discrete systems robust stability,Automatika,4,,,1990,3,9,,1,0,

,11,0,0,0,0,0,Polyak B.T.,Tsypkin Y. Z.,,Frequency criteria for robust stability and aperiodicity of linear systems,Autom. Remote Control,51,,,1990,1192,1200,,1,0,

,11,0,0,0,0,0,Jury E.I.,,,Discrete system robustness: a survey,Autom. Remote Control,51,,,1990,571,592,,1,0,

,13,0,0,0,0,0,Read C.B.,,,Articles on the history of Mathematics:…,School Sci. Math.,59,,,1959,689,717,Contains a bibliography: several articles on polynomials mentioned,1,0,

,19,0,0,0,0,0,Natucci,,,Storia della teoria delle equazioni,Period. Mat. Ser. 4,42,,,1964,277,290,Ancient treatment of quadratic and cubic,1,0,

,19,0,0,0,0,0,Casara G.,,,Un problema archimedeo di 3^o grado e le sue soluzioni attraverzo I tempi,Boll Unione Mat. Ital. Ser. 2,4,,,1942,244,262,Treats history of special cubic related to volume of a sphere,1,0,

,29,0,0,0,0,0,von Sanden H.,,,Quadratwurzel mit der Rechenmaschine,Zeit. Angew. Math. Mech.,38,,,1958,71,0,Square root with a calculator,1,0,

,2,4,7,17,0,0,Schultz G.,,,Formelsammlung zur praktischen Mathematik,,,,Berlin,1945,0,0,Treats Newton, Graeffe, reguli falsi, evaluation,1,0,

,2,10,14,17,19,29,Butler R.,Kerr E.,,An Introduction to Numerical Methods,,,Pitman,London,1967,0,0,Treats Newton, Descartes, Bairstow, Horner, low degree, surds,1,0,

,2,4,7,0,0,0,Redish K.A.,,,Introduction to Computational Methods,,,English University Press,,1961,0,0,Treats Newton, Graeffe, reguli falsi,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,Invariance of the strict Hurwitz property for Polynomials with perturbed coefficients,IEEE Trans. Automat. Control,29,,,1984,935,936,,1,0,

,19,0,0,0,0,0,Struik D.J.,,,On ancient Chinese Mathematics,Math. Teacher,56,,,1963,424,0,Horner's method for quadratic discovered by Chinese,1,0,

,19,0,0,0,0,0,Terquem O.,,,'Arithmétique et algèbre des Chinois' par M.K.L. Biernatzki,Nouv. Ann. Math,2,,,1862,529,540,Early chinese treatment of quartic,1,0,

,29,0,0,0,0,0,Treutlein P.,,,Das Rechnen in 16. Jahrhundert,Abh. Gesch. Math.,1,,,1877,64,65,Early square root,1,0,

,19,0,0,0,0,0,Sédillot L.,,,Matériaux pour servir á l'histoire comparée des sciences mathématiques chez les Grecs et les Orientaux. 2 vols.,,,,Paris,1849,0,0,,1,0,

,19,29,0,0,0,0,Mikami Y.,,,The influence of Abaci on the Chinese and Japanese Mathematics,Jahresb. Deutsch. Math.-Verein..,20,,,1911,380,393,Roots, quadratics, and cubics by abacus,1,0,

,29,0,0,0,0,0,Lam L.Y.,,,On the existing fragments of Yang Hui's "Hsiang Chieh Suan Fa",Arch. Hist. Exact Sci.,6-1,,,1969,82,88,Chinese treatment of fourth root,1,0,

,19,0,0,0,0,0,Karpinski L.C.,,,The Algebra of Abu Kamil,Amer. Math. Monthly,21 (2),,,1914,37,0,Quadratics among the Arabs,1,0,

,19,25,0,0,0,0,Betti E.,,,Opere matematiche,,,Hoepli,Milano,1903,0,0,Considers solution by radicals, and cubics,1,0,

,19,0,0,0,0,0,Bortolotti E.,,,Storia della matematica elementare, in Enciclopedia delle Matematiche Elementari, ed L. Berzolari,,,Hoepli,Milano,1962,0,0,Includes history of low-degree polynomials,1,0,

,1,2,7,14,26,0,Beckett R.,Hurt J.,,Numerical Calculations and Algorithms,,,McGraw-Hill,New York,1967,0,0,Treats bisection, Newton, secant, Muller, Bairstow, error estimation,1,0,

,19,0,0,0,0,0,van Hée L.,,,Li Yeh, mathématicien chinois du III^e siècle,T'oung Pao Ser. 2,14,,,1913,537,568,Early quadratic,1,0,

,29,0,0,0,0,0,Bruins E.M.,,,Some Mathmatical Texts,Sumer,10,,,1954,55,61,Square and cube roots,1,0,

,19,0,0,0,0,0,Taha Baqir,,,Another important mathematical text from Tell Harmal,Sumer,6,,,1950,130,147,Ancient quadratics,1,0,

,29,0,0,0,0,0,Bruins E.M.,,,Revision of the mathematical texts from Tell Harmal,Sumer,9,,,1953,241,251,sqrt(2),1,0,

,1,2,7,14,15,0,Al-Khafaji A. W.,Tooley J.R.,,Numerical Methods in Engineering Practise,,,Holt, Rinehart & Winston,New York,1986,0,0,Treat bisection, Newton, reguli falsi, a second derivative method, and Bairstow,1,0,

,1,2,7,0,0,0,Atkinson K.E.,,,An Introduction to Numerical Analysis 2/E,,,Wiley,New York,1985,0,0,Treats bisection, Newton, secant,1,0,

,19,0,0,0,0,0,Rodet L.,,,L'Algèbre d'Al-Kharizmi,J. Asiatique Ser. 7,11,,,1878,38,0,early quadratic,1,0,

,19,0,0,0,0,0,Nasr S.H.,,,Science and Civilization in Islam,,,Harvard Univ. Press,,1968,158,0,brief quadratics,1,0,

,2,4,14,19,0,0,Salvadori M.G.,Baron M.L.,,Numerical Methods in Engineering 2/E,,,Prentice Hall,Englewood Cliffs NJ,1961,0,0,Treats Newton, Graeffe, Bairstow, quartic,1,0,

,1,2,3,7,17,19,Guggenheimer H.,,,BASIC Mathematical Programs for Engineers and Scientists,,,Petrocelli Books,West Hempstead NY,1987,0,0,Treats bisection, Newton, secant, Muller, simultaneous method, cubic,1,0,

,1,2,7,17,0,0,Hopkins T.,Philips C.,,Numerical Methods in Practise using the NAG Library,,,Addison-Wesley,Reading Mass,1988,0,0,Treats bisection, Newton, secant, evaluation,1,0,

,1,2,7,14,24,0,Hultquist P.F.,,,Numerical Methods for Engineers and Computer Scientists,,,Benjamin/ Cummings,Menlo Park, Cal,1988,0,0,Treats bisection, Newton, secant, acceleration, Bairstow,1,0,

,19,0,0,0,0,0,Gulibeau L.,,,The History of the Solution of the cubic equation,Nat. Math. Mag,5(4),,,1930,8,12,Title says it,1,0,

,1,2,7,14,19,0,Tuma J.J.,,,Handbook of Numerical Calculations in Engineering,,,McGraw-Hill,New York,1989,0,0,Treats bisection, Neton, secant, low-degree, Bairstow,1,0,

,1,2,7,0,0,0,Turner P.R.,,,Guide to Numerical Analysis,,,CRC Press,Boca Raton, Fla,1989,0,0,Treats bisection, Newton, secant,1,0,

,2,7,0,0,0,0,Wilkes M.V.,,,A Short Introduction to Numerical Analysis,,,CUP,New York,1966,0,0,Treats Newton, reguli falsi,1,0,

,25,0,0,0,0,0,Tannery J.,,,Manuscrits d'Évariste Galois,,,Gauthier-Villars,Paris,1908,0,0,,1,0,

,25,0,0,0,0,0,Tannery J.,,,Manuscrits et papiers inéditée de Galois,Bull. Sci. Math.,,,,1907,275,308,,1,0,

,19,0,0,0,0,0,Heiberg J.L.,,,Geschichte der Mathematik und Naturwissenschaften in Altertum,,,,Munchen,1925,0,0,Ancient quadratic,1,0,

,19,25,0,0,0,0,Bashmakova I.,Smirnova G.,,The Beginnings and Evolution of Algebra,,,Math. Assoc. Amer,,2000,0,0,History of low-degree, existence, solution by radicals,1,0,

,3,0,0,0,0,0,Wu X.,,,On zeros of a polynomial and vector solutions of associated polynomial systems from Vieta theorem.,Appl. Numer. Math.,44,,,2003,415,423,uses Broyden's method for the system. Claims better for multilpe zeros,1,0,

,3,0,0,0,0,0,Kjurkchiev N.,Iliev A.,,On the R-order of convergence of a family of methods for simultaneous extraction of part of all roots of algebraic polynomials,BIT,42,,,2002,879,885,Durand-Kerner method modified for a few roots.,1,0,

,2,19,29,0,0,0,Reynaud A.A.L.,,,Traité d'algèbre,,,,Paris,1821,0,0,Treats Newton, surds, quadratics,1,0,

,2,4,7,10,19,0,Mineur H.,,,Techniques de Calcul Numérique,,,Dunod,Paris,1966,0,0,Treats Newton, Graeffe, Sturm, secant, low-degree,1,0,

,19,0,0,0,0,0,Ruska J,,,Zur altesten arabischen Algebra und Rechenkunst,Sitz. Heidelberger Akad. Wiss.,8(2),,,1917,1,125,Arabic quadratics,1,0,

,10,25,0,0,0,0,de Comberousse C.,,,Cours de Mathématiques,,,Gauthier-Villars,Paris,1890,0,0,Treats existence, solution by radicals, Sturm, etc.,1,0,

,0,0,0,0,0,0,de Goeje,,,Annales quas scripsit.. Djarin al-Tabari,,,,,0,0,0,,1,0,

,25,0,0,0,0,0,De Peslouan C.L.,,,N.-H. Abel--sa vie et son oeuvre,,,Gauthier-Villars,Paris,1906,0,0,Touches on solution by radicals,1,0,

,2,4,10,19,25,0,Derwidué L.,,,Introduction á l'algèbre supérieure et au calcul numérique,,,Masson,Paris,1957,0,0,Treat Newton, Graeffe, Sturm etc, low-degree, existence,1,0,

,19,0,0,0,0,0,Story W.E.,,,Omar Khayyam as a mathematician,,,Rosemary Press,,1918,0,0,Very brief treatment of cubic,1,0,

,19,29,0,0,0,0,Juschkewitsch A.P.,Rosenfeld B.A.,,Die mathematik der Lander des Ostens im Mittelalter,,,,Berlin,1963,0,0,Treats quadratic, other low-degree equations, and surds,1,0,

,2,10,19,25,0,0,Cipolla M.,,,Analisi Algebrica,,,,,0,0,0,Treats Sturm etc, Newton, existence, low-degree,1,0,

,10,0,0,0,0,0,Yap C.K.,,,Fundamental Problems of Algorithmic Algebra,,,Oxford,,1999,0,0,,1,0,

,23,0,0,0,0,0,Ghersi I.,,,Matematica dilettevole e curiosa,,,Hoepli,Milano,1978,0,0,Section on mechanical devices,1,0,

,3,0,0,0,0,0,Illief L,Dochev,,Uber Newtonsche Iterationen,Wiss. Zeit. Tech. Hochsch. Dres.,12,,,1963,117,118,Original paper on simultaneous methods.,1,0,

,11,0,0,0,0,0,Routh E.J.,,,Stability of Motion ed. A.T.Fuller,,,Taylor & Francis,London,1975,0,0,,1,0,

,10,19,0,0,0,0,Mayer,Choquet C,,Traité élémentaire d'agèbre,,,,Paris,1832,0,0,Early statement of Sturm's Theorem. Also low-degree.,1,0,

,10,0,0,0,0,0,Porter M.B.,,,On the roots of functions connected to a linear recurrent relation of the second order,Ann. Math. Ser. 2,3,,,1901,55,70,Treats Sturm's Theorem,1,0,

,21,0,0,0,0,0,Driver K,Duren P,,Asymptotic zero distribution of hypergeometric polynomials,Numerical Algorithms,21,,,1999,147,156,,1,0,

,11,0,0,0,0,0,Bialas S,Garloff J,,Convex combinations of stable polynomials,J. Franklin Inst.,319,,,1985,373,377,,1,0,

,11,0,0,0,0,0,Peterson I.R.,,,A class of stability regions for which a Kharitonov type theorem holds,IEEE Trans. Automat. Control,34,,,1989,1111,1115,,1,0,

,11,0,0,0,0,0,Peterson I.R.,,,A new extension to Kharitonov's theorem,Proc. 26th IEEE Conf. Decision a Control,,,,1987,2070,2075,,1,0,

,11,0,0,0,0,0,Djaferis T.E.,Hollot C.V.,,The stability of a family of polynomials can be deduced from a finite number O(k³) of frequency checks,IEEE Trans. Automat. Control,34,,,1989,982,992,,1,0,

,11,0,0,0,0,0,Djaferis T.E.,Hollot C.V.,,Parameter partitioning via shaping conditions for the stability of families of polynomials,IEEE Trans. Automat. Control,34,,,1989,1205,1209,,1,0,

,11,0,0,0,0,0,Soh Y.C.,Foo Y.K.,,On the existence of strong Kharitonov theorems for interval polynomials,Proc. IEEE Conf Decision and Control,,,,1989,1882,1887,,1,0,

,11,0,0,0,0,0,Katbab A,Jury E.I.,,Robust Schur stability of a complex-coeffecient polynomial set with coefficients in a diamond,J. Franklin Inst.,327,,,1990,687,698,,1,0,

,11,0,0,0,0,0,Xie X.K.,,,Stable polynomials with complex coefficients,Proc. 24th IEEE Conf. Decision Contr.,,,Fort Lauderdale, FL,1985,324,325,,1,0,

,11,0,0,0,0,0,Hollot C.V.,Looze D.P.,Bartlett A.C.,Unmodeled dynamics: performance and stability via parameter space methods,Proc. 26th Conf. On Decision and Contr.,,,Los Angeles, CA,1987,2076,2081,,1,0,

,11,0,0,0,0,0,Kraus F,Anderson B.D.O.,Mansour M,Robust Schur polynomial stability and Kharitonov's theorem,Proc. IEEE Contr. And Decision Conf.,,,Los Angeles, CA,1987,2088,2095,,1,0,

,2,0,0,0,0,0,Pall G.A.,,,Introduction to Scientific Computing,,,Appleton-Century-Crofts,NY,1971,0,0,Brief treatment of Newton's method,1,0,

,10,13,19,25,0,0,Smith D.E.,,,A Source Book in Mathematics,,,McGraw-Hill,New York,1929,0,0,Original articles on cubic, quartic, quintic, fundamental theorem, Homer's method,1,0,

,29,0,0,0,0,0,Shen K.S.,Crossley J.N.,Lun W.-C.,The nine chapters on the mathematical art, companion and commentary,,,,Oxford,1999,0,0,Brief treatment of square and cube roots,1,0,

,19,0,0,0,0,0,Hölder O,,,Über den Casus Irreducibiles bei der Gleichung dritten Grades,Math. Ann.,38,,,1891,307,312,Treats irreducible case of cubic,1,0,

,18,0,0,0,0,0,Neumaier A,,,Enclosing clusters of zeros of polynomials,J. Comput. Appl. Math.,156,,,2003,389,401,A posteriori error bounds based on Gershgorin's theorem. Works well for multiple zeros and clusters.,1,0,

,18,0,0,0,0,0,Rump S.M.,,,Ten methods to bound multiple roots of polynomials,J. Comput. Appl. Math.,156,,,2003,403,432,Given k-fold root, finds a disk having ≥ k roots in it.,1,0,

,15,0,0,0,0,0,Amat S,Busquier S,Gutierrez J.M.,Geometric constructions of iterative functions to solve nonlinear equations,J. Comput. Appl. Math.,157,,,2003,197,205,Treats third order methods.,1,0,

,15,0,0,0,0,0,Homeier H.H.H.,,,A modified Newton method for rootfinding with cubic convergence,J. Comput. Appl. Math.,157,,,2003,227,230,Third order, but requires 3 function evaluations per step.,1,0,

,28,0,0,0,0,0,Pereira R,,,Differentatiors and the geometry of polynomials,J. Math. Anal. Appl.,285,,,2003,336,348,Relates roots to those of derivative.,1,0,

,13,0,0,0,0,0,Sasaki T,Terui A,,A formula for separating small roots of a polynomial,Sigsam Bull.,36 (3),,,2002,19,23,Title says it.,1,0,

,18,0,0,0,0,0,Cao J,Gardner R,,Restrictions on the zeros of a polynomial as a consequence of conditions on the coefficients of even powers and odd powers of the variable.,J. Comput. Appl. Math.,155,,,2003,153,162,Generalizes Kakeya-Enestrom theorem.,1,0,

,19,0,0,0,0,0,Guimares R,,,Sur la vie et l'oeuvre de Pedro Nunes,,,Univ. de Coimbre,,1915,0,0,Early quadratic.,1,0,

,21,0,0,0,0,0,Walker P,,,The zeros of the partial sums of the exponential series,Amer. Math. Monthly,110,,,2003,337,339,Gives bounds for mentioned zeros.,1,0,

,13,0,0,0,0,0,Minac J,,,Newton's identities once again,Amer. Math. Monthly,110,,,2003,232,234,New proof of sums of d'th powers of roots of polynomials of degree n, where d < n.,1,0,

,1,2,7,0,0,0,Jacques I,Judd C,,Numerical Analysis,,,Chapman and Hall,New York,1987,0,0,Treats bisection, Newton, Secant, reguli falsi,1,0,

,1,2,7,18,14,15,Kincaid D,Cheney W,,Numerical Analysis Mathematics of Scientific Computing,,,Brooks/Cole,Pacific Grove, Calif,1991,0,0,Treats bisection, Newton, Secant, bounds, Bairstow, Laguerre.,1,0,

,1,2,7,0,0,0,Kreyszig E,,,Advanced Engineering Mathematics, 5th ed.,,,John Wiley,New York,1983,0,0,Brief treatment of bisection, Newton, and reguli falsi,1,0,

,13,0,0,0,0,0,Sheil-Small T.,,,Complex Polynomials,,,Cambridge Univ. Press,,2002,0,0,Rather theoretical,1,0,

,25,0,0,0,0,0,Stewart I,,,Galois Theory 3rd Edition.,,,,,0,0,0,Existence and solution by radicals,1,0,

,10,0,0,0,0,0,Zarowski C.J.,Ma X,Fairman F.W.,QR-factorization method for computing the greatest common divisor of polynomials with inexact coefficients,IEEE Trans. Signal Proc.,48,,,2000,3042,3051,GCD is contained in last row of R in the QR-factorization of a near-Toeplitz matrix derived from the Sylvester matrix,1,0,

,22,0,0,0,0,0,Krandick W,,,"Trees and jumps and real roots",J. Comput. Appl. Math.,162,,,2004,51,55,NB Improvement on Descartes' method for real roots.,1,0,

,30,0,0,0,0,0,Bini D.A.,Böttcher A,,Polynomial factorization through Toeplitz matrix computations,Lin. Alg. Appl.,366,,,2003,25,37,Title says it.,1,0,

,3,0,0,0,0,0,Iliev A.I.,Kyurkchiev N.V.,,On a generalization of the Obreshkoff-Ehrlich method for simultaneous inclusion of only part of all multiple roots of algebraic polynomials,Comput. Math. Math. Phys.,43,,,2003,482,488,Cubic order if multiplicities known,1,0,

,7,0,0,0,0,0,Wu X,Shen Z,Xia J,An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations,Appl. Math. Comput.,144,,,2003,381,388,Variation on Steffensen's method. Two function evaluations per step give quadratic convergence.,1,0,

,7,0,0,0,0,0,Amat S,Busquier S,,On a higher-order Secant method,Appl. Math. Comput.,141,,,2003,321,329,Modified Secant method has order 2,1,0,

,11,0,0,0,0,0,Argoun M.B.,,,Stability of Hurwitz polynomials under coefficient perturbations: necessary and sufficient conditions,Internat. J. Control,45,,,1987,739,744,Considers case of different coefficients having different degrees of uncertainty.,1,0,

,11,0,0,0,0,0,Anderson B.D.O.,Jury E.I.,Mansour M,On robust Hurwitz polynomials,IEEE Trans. Automatic Control,32,,,1987,909,913,For n=3,4,5 the number of polynomials needed to check robust stability is 1,2,3. For n ≥ 6 it is 4.,1,0,

,11,0,0,0,0,0,Mori T,Kokame H,,A necessary and sufficient condition for stability of linear discrete systems with parameter variations,J. Franklin Institute,321,,,1986,135,138,,1,0,

,11,0,0,0,0,0,Delansky J.F.,Bose N.K.,,Schur stability and stability domain construction,Internat. J. Control,49,,,1989,1175,1183,,1,0,

,11,0,0,0,0,0,Yeung K.S.,,,Linear discrete system stability under parameter variations,Internat. J. Control,40,,,1984,855,862,,1,0,

,11,0,0,0,0,0,Minichelli R.J.,Anagnost J.J.,Desoer C.A.,An elementary proof of Kharitonov's stability theorem with extensions,IEEE Trans. Automat. Control,34,,,1989,995,998,,1,0,

,11,0,0,0,0,0,Delansky J.F.,Bose N.K.,,Real and complex polynomial stability domain construction via network realizability theory,Internat. J. Control,48,,,1988,1343,1349,,1,0,

,10,0,0,0,0,0,Karcanias N,Mitrouli M,,Normal factorization of polynomials and computational issues,Comput. Math. Appls.,45,,,2003,229,245,Determines multiplicities, uses GCD.,1,0,

,17,0,0,0,0,0,Barrio R,,,A unified rounding error bound for polynomial evaluation,Adv. Comput. Math.,19,,,2003,385,399,Treats various non-standard bases.,1,0,

,26,0,0,0,0,0,Winkler J.R.,,,A statisical analysis of the numerical condition of multiple roots of polynomials,Comput. Math. Appl.,45,,,2003,9,24,Shows that componentwise and normwise condition estimates may vary by several orders of magnitude.,1,0,

,25,0,0,0,0,0,Derksen H,,,The fundamental theorem of algebra and linear algebra,Amer. Math. Monthly,110,,,2003,620,623,Treats existence. Advanced.,1,0,

,18,11,28,0,0,0,Dieudonné M.J.,,,La théorie analytique des polynomes d'une variable (á coefficients quelconques),Mem. Sci. Math.,93,,Paris,1938,0,0,Mostly about bounds, and derivatives,1,0,

,1,2,7,14,0,0,Kuo S.S.,,,Numerical Methods and Computers,,,Addison-Wesley,Reading, Mass.,1965,0,0,Treats bisection, Newton, Reguli Falsi, and Bairstow,1,0,

,2,16,0,0,0,0,Lieberstein H.M.,,,A Course in Numerical Analysis,,,Harper & Row,New York,1968,0,0,Treats Newton, convergence.,1,0,

,1,2,12,0,0,0,Moore R.E.,,,Mathematical Elements of Scientific Computing,,,Holt, Rinehart & Winston,New York,1975,0,0,Describes bisection, Newton, and Interval Newton.,1,0,

,2,4,6,14,17,19,Froberg C.E.,,,Introduction to Numerical Analysis,,,Addison-Wesley,Reading, Mass.,1969,0,0,Treats Newton, Graeffe, QD, Bairstow, Homer, and low-degree.,1,0,

,2,7,4,14,5,6,Haggerty G.B.,,,Elementary Numerical Analysis with Programming,,,Allyn and Bacon,Boston,1972,0,0,Treats Newton, QD, Lehmer, Graeffe, Secant, and Bairstow,1,0,

,1,2,7,4,14,16,Jain M.K.,Inyengar S.R.K.,Jain R.K.,Numerical methods for scientific and engineering computations,,,Halstead,New York,1982,0,0,Treats bisection, Newton, Secant, Muller, Graeffe, Bairstow, convergence, acceleration,1,0,

,2,14,0,0,0,0,Jensen J.A.,Rowland J.H.,,Methods of Computation: The Linear Space Approach to Numerical Analysis,,,Scott, Foresman,Glenview, Ill.,1975,0,0,Treats Newton, Bairstow,1,0,

,11,0,0,0,0,0,Barmish B.R.,Tempo R,,On the spectral set for a family of polynomials,IEEE Trans. Automat. Control,AC-36,,,1991,111,115,,1,0,

,11,0,0,0,0,0,Barmish B.R.,Khargonekar P.P.,Shi Z.C. and Tempo R,Robustness margins need not be continuous function of problem data,Systems Control Lett.,15,,,1990,91,99,,1,0,

,11,0,0,0,0,0,Anderson B.D.O.,,,The reduced Hermite criterion with application to proof of the Lienard-Chipart criterion,IEEE Trans. Automat. Control,17,,,1972,669,672,,1,0,

,11,0,0,0,0,0,Barmish B.R.,DeMarco C.L.,,Criteria for robust stability of systems with structured uncertainty: a perspective,Proc. Of the Amer. Contr. Conf.,,,Minneapolis, MN,1987,476,481,,1,0,

,11,0,0,0,0,0,Peterson I.R.,,,A new extension to Kharitonov's theorem,Proc. 26th IEEE Conf. Decision and Contr.,,,Los Angeles, CA,1987,2070,2075,,1,0,

,11,0,0,0,0,0,Chapellat H,Bhattacharyya S.P.,,Some recent results in structured robust stability: an overview,Int. J. Adaptive Contr. And Signal Processing,2,,,1988,311,325,,1,0,

,11,0,0,0,0,0,Vicino A,,,Maximal polytopic stability domains in parameter space for uncertain systems,Internat. J. Control,49,,,1989,351,361,,1,0,

,19,29,0,0,0,0,Peacock G,,,A Treatise on Mathematics,,,Scripta Mathematica,New York,1940,0,0,Treats low-degree and square roots,1,0,

,20,0,0,0,0,0,Arvesu J,Alvarez-Wodarse R,Marcellan F and Pan K,Jacobi-Sobolev type orthogonal polynomials: second-order differential equations and zeros,J. Comput. Appl. Math.,90,,,1998,135,156,,1,0,

,11,0,0,0,0,0,Benedir M,Picinbono B,,Comparison between some stability criteria of discrete time filters,IEEE Trans. Acous. Speech Sig. Proc.,36,,,1988,993,1001,,1,0,

,11,0,0,0,0,0,Djaferio T.J.,,,Shaping conditions for the robust stability of polynomials with multilinear parameter uncertainty,Proc. 27th IEEE Conf. Dec. Control,,,,1988,526,531,,1,0,

,11,0,0,0,0,0,Chapellat H et al,,,Stability margins for Hurwitz polynomials,Proc. 27th IEEE Conf. Dec. Control,,,,1988,1392,1398,,1,0,

,19,0,0,0,0,0,Lorey W,,,On Diefenbach's method for the solution of biquadratics,National Math. Mag.,11,,,1937,216,220,Early 19th century treatment of quartic,1,0,

,21,0,0,0,0,0,Driver K.,Jordaan K.,,Zeros of ₃F₂(-n,b,c:z:d,e) polynomials,Numer. Alg.,30,,,2002,323,333,Zeros of hypergeometric polynomials,1,0,

,19,0,0,0,0,0,Busard H.L.L.,,,Quelques sujets d'histoire des mathématiques au moyen-age,,,,Paris,1968,0,0,Treats quadratic and some special cubics in middle ages.,1,0,

,19,0,0,0,0,0,Boyer C.B.,,,Cartesian and Newtonian Algebra in mid-eighteenth century, in "Actes du XI^e Congrès International d'Histoire des Sciences V3" ed B. Suchodolski,,,,Warsaw,1968,0,0,Brief treatment of low-degree equations,1,0,

,18,0,0,0,0,0,Diaz-Barrero J.L.,,,An annulus for the zeros of polynomials,J. Math. Anal. Appl.,273,,,2002,349,352,Proves bounds containing binomial coefficients and Fibonacci numbers,1,0,

,1,2,7,14,16,19,La Fara R.L.,,,Computer Methods for Science and Engineering,,,Hayden,Rochelle Pk, NJ,1973,0,0,Treats bisection, Newton, secant, Lin-Bairstow, convergence, low-order quite well,1,0,

,19,29,0,0,0,0,Peacock G,,,A Treatise on Algebra, Vols 1, 2,,,,New York,1940,0,0,Treats low-degree, surds,1,0,

,25,0,0,0,0,0,Redfield R.H.,,,Abstract Algebra: A Concrete Introduction,,,Addison-Wesley,,2001,0,0,Proves insolubility by radicals,1,0,

,21,0,0,0,0,0,Cayley A.,,,On the Binomial Equation x^p-1 = 0,Proc. London Math. Soc,11,,,1880,4,17,,1,0,

,21,0,0,0,0,0,Cayley A.,,,On the Binomial Equation x^p-1 = 0;quinquisection,Proc. London Math. Soc.,12,,,1881,15,16,,1,0,

,21,0,0,0,0,0,Rogers L.J.,,,Note on the Quinquisectional Equation,Proc. London Math. Soc.,32,,,1900,199,207,,1,0,

,21,0,0,0,0,0,Burnside W.,,,On Cyclotomic Quinquisection,Proc. London Math. Soc. Ser. 2,14,,,1915,251,259,,1,0,

,21,0,0,0,0,0,Uphadhyaya P.O.,,,Cyclotomic quinquisection for every prime of the form 10n+1 between 100 and 500,Proc. London Math. Soc. Ser. 2,20,,,1922,494,496,,1,0,

,21,0,0,0,0,0,Cayley A.,,,On the equation x¹⁷-1 = 0,Collected Mathematical Papers,13,,Cambridge,1897,60,63,Also p 66,1,0,

,21,0,0,0,0,0,Schumacher J.,,,Die Auflösung der Gleichung x²⁵⁷-1 = 0,Arch. Math. Phys. Ser. 3,20,,,1913,295,311,,1,0,

,21,0,0,0,0,0,Driver K.,Möller M.,,Quadratic and cubic transformations and zeros of hypergeometric polynomials,J. Comput. Appl. Math.,142,,,2002,411,417,,1,0,

,19,25,0,0,0,0,Miller G.A.,Blichfield H.F.,Dickson L.E.,Theory and Applications of Finite Groups,,,Wiley,New York,1916,0,0,Considers solubility by radicals; also cubic and quartic,1,0,

,13,0,0,0,0,0,Encontre D.,,,Mémoire sur les principes fondamentaux de la théorie générale des équations,Ann. Math. Pures Appl.,4,,,1813,201,222,,1,0,

,15,0,0,0,0,0,Elgin D.,,,A third-order iterative scheme,Math. Gaz.,86,,,2002,126,128,Derives a 3rd-order method involving f''. No discussion of efficiency,1,0,

,2,0,0,0,0,0,Wendroff B.,,,First Principles of Numerical Analysis,,,Addison-Wesley,,1969,0,0,Treats Newton's method,1,0,

,2,19,0,0,0,0,Watson, W.A.,Philipson T.,Oates P.J.,Numerical Analysis-the Mathematics of Computing,,,Edward Arnold,London,1969,0,0,Treats Newton, quadratic,1,0,

,2,4,7,11,17,19,Zurmühl R.,,,Praktische Mathematik für Ingenieure und Physiker,,,Springer,Berlin,1965,0,0,Treats Newton, Graeffe, interpolation, low-degree, evaluation,1,0,

,19,0,0,0,0,0,McClintock E.,,,On a solution of the biquadratic which combines the methods of Descartes and Euler,Bull. Amer. Math. Soc. Ser 2,3,,,1897,389,390,Reduces it to a cubic,1,0,

,19,0,0,0,0,0,Hamilton A.,,,The irreducible case of the cubic equation,Ann. Math. Ser. 2,1,,,1899,41,45,,1,0,

,21,0,0,0,0,0,Segura J,,,The zeros of special functions from a fixed point method,SIAM J. Numer. Anal.,40,,,2002,114,133,,1,0,

,21,0,0,0,0,0,Cantero M.J.,Moral L,Velázquez L,Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle,Lin. Alg. Appl.,362,,,2003,29,56,Uses Laurent polynomials,1,0,

,11,0,0,0,0,0,Dabke K.P.,,,A simple criterion for stability of linear discrete systems,Internat.. J. Contr.,37,,,1983,657,659,Uses Eigenvalues to ensure poles within a certain circle,1,0,

,11,0,0,0,0,0,Fu M,Olbrot A.W.,Polis M.P.,Introduction to the parametric approach to robust stability,IEEE Contr. Sys. Mag.,9 (5),,,1989,7,11,This is a Review,1,0,

,11,0,0,0,0,0,Chapellat H,Bhattacharyya S.P.,Keel L.H.,Stability margins for Hurwitz polynomials,Proc. 27th IEEE Conf. Decision Contr.,,,Austin, Texas,1988,1392,1398,,1,0,

,4,2,10,19,22,25,Uspensky J.V.,,,Theory of Equations,,,McGraw-Hill,New York,1948,0,0,Treats Newton, Graeffe, Sturm and GCD, low-order, Vincent, existence,1,0,

,21,0,0,0,0,0,Driver K,Möller M,,Zeros of the hypergeometric polynomial F(-n,b;-2n;z),J. Approx. Theory,110,,,2001,74,87,As n → ∞ the zeros approach the Cassini curve.,1,0,

,10,0,0,0,0,0,von zur Gathen J,Lücking T,,Subresultants revisited,Theor. Comput. Sci.,297,,,2003,199,239,Also treats polynomial remainder sequences,1,0,

,10,0,0,0,0,0,Ho C,Yap C.K.,,The Habicht approach to subresultants,J. Symb. Comput.,21,,,1996,1,14,Treats "pseudo"-subresultants,1,0,

,18,0,0,0,0,0,Linden H,,,Numerical radii of some companion matrices and bounds for the zeros of polynomials in "Analytic and Geometric Inequalities and Applications" (eds T.M. Rassias, H.M. Srivastava),,,Kluwer,Dordrecht,1999,205,229,Title says it.,1,0,

,10,11,0,0,0,0,Balinskii A.I.,Podlevskii B.M.,,Computational aspects of the application of Frobenius matrix to separation of roots of polynomials,Zh. Vychisl. Mat. Mat. Fiz.,39,,,1999,1069,1073,Considers common roots and stability,1,0,

,3,0,0,0,0,0,Petkovic M.S.,,,On initial conditions for the convergance of simultaneous root finding methods,Computing,57,,,1996,163,177,Computable conditions for convergence,1,0,

,3,0,0,0,0,0,Petkovic M.S.,,,A family of simultaneous zeros-finding methods,Comput. Math. Appl.,34-10,,,1997,49,59,Fourth-order simultaneous method,1,0,

,1,2,7,0,0,0,Chapra S.C.,Canale R.P.,,Numerical Methods for Engineers,,,McGraw-Hill,New York,1985,0,0,Treats bisection, Secant, Newton,1,0,

,5,0,0,0,0,0,Suzuki T,Suzuki T,,Numerical integration error method for zeros of analytic functions,J. Comput. Appl. Math.,152,,,2003,493,505,,1,0,

,5,0,0,0,0,0,Sakurai T et al,,,An error analysis of two related quadrature methods for computing zeros of analytic functions,J. Comput. Appl. Math.,152,,,2003,467,480,Uses trapezoidal rule for quadrature,1,0,

,3,12,0,0,0,0,Petkovic M.S.,,,Laguerre-like inclusion methods for polynomial zeros,J. Comput. Appl. Math.,152,,,2003,451,465,Simultaneous inclusion methods of fourth order,1,0,

,16,21,0,0,0,0,Herzberger J,,,Explicit bounds for the positive root of classes of polynomials with applications,J. Comput. Appl. Math.,152,,,2003,187,198,Used in estimating order of convergence and in finance,1,0,

,1,2,7,14,17,0,Yakowitz S,Szidarovszky F,,An Introduction to Numerical Computations,,,Macmillan,New York,1986,0,0,Treats bisection, Newton, Secant, Bairstow, and evaluation.,1,0,

,21,0,0,0,0,0,goebel,Buendía E,Dehesa J.S.,On the distribution of zeros of the generalized q-orthogonal polynomials,J. Phys. A. Math. Gen.,30,,,1997,6743,6768,,1,0,

,21,0,0,0,0,0,Dragnev P.D.,Saff E.B.,,A problem in potential theory and zero asymptotics of Krawtchouk polynomials,J. Approx. Theory,102,,,2000,120,140,,1,0,

,21,0,0,0,0,0,Falday J,Gawronski W,,On the limit distribution of the zeros of Jonquiére polynomials and generalized classical orthogonal polynomials,J. Approx. Theory,81,,,1995,231,249,,1,0,

,21,0,0,0,0,0,Kuijlaars A.B.J.,Rakhmanov E.A.,,Zero distribution for discrete polynomials,J. Comput. Appl. Math.,99,,,1998,255,274,,1,0,

,21,0,0,0,0,0,Kuijlaars A.B.J.,van Assche W,,The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients,J. Approx. Theory,99,,,1999,167,197,,1,0,

,21,0,0,0,0,0,Lang W,,,On sums of powers of zeros of polynomials,J. Comput. Appl. Math.,89,,,1998,237,256,Considers Chebyshev and other orthogonal polynomials,1,0,

,11,0,0,0,0,0,Yang X,,,Necessary conditions of Hurwitz polynomials,Lin. Alg. Appl.,359,,,2003,21,27,,1,0,

,7,0,0,0,0,0,Zhu Y,Wu X,,A free-derivative method of order three having convergence of both point and interval for non-linear equations,Appl. Math. Comput.,137,,,2003,49,55,Generalized Secant method,1,0,

,3,0,0,0,0,0,Sun F,Zhang X,,A new method of increasing the order of convergence step by step,Appl. Math. Comput.,137,,,2003,15,32,Describes some very high order simultaneous methods,1,0,

,20,0,0,0,0,0,Blake I,Gao S,Lambert R,Constructive problems for irreducible polynomials over finite fields in "Information Theory and Applications" (eds A. Gulliver and N. Secord),Lecture Notes in Computer Science,793,Springer-Verlag,,1994,1,23,,1,0,

,13,0,0,0,0,0,Bertuello B,,,Problem 33.2,Math. Spectrum,33,,,2001,20,20,,1,0,

,3,12,0,0,0,0,Petkovic M.S.,,,Laguerre-like inclusion method for polynomial zeros,J. Comput. Appl. Math,152,,,2003,451,465,Simultaneous inclusion methods. Converges if verifiable conditions satisfied.,1,0,

,20,0,0,0,0,0,Fleischmann P,Roelse P,,Comparative implementations of Berlekamp's and Niederreiter's polynomial factorization algorithms in "Finite Fields and Applications, Proc. 3rd Internat. Conf." (eds S. Cohen and H. Niederreiter),London Math. Soc. Lecture Notes Ser.,233,Cambridge University Prs.,London,1996,73,83,,1,0,

,20,0,0,0,0,0,Gao S,von zur Gathen J,,Berlekamp's and Niederreiter's polynomial factorization algorithms in "Finite Fields: Theory, Applications and Algorithms" (eds G.L. Mullen and P.J.S. Shine),,,AMS,,1994,101,115,,1,0,

,21,0,0,0,0,0,Boyd D.W.,,,On a problem of Byrnes concerning polynomials with restricted coeffecients,Math. Comp.,66,,,1997,1697,1703,Deals with polynomials having coefficients ±1, and an m-fold zero at 1.,1,0,

,17,0,0,0,0,0,Sameh A.H.,,,Numerical parallel algorithms: a survey, in "High Speed Computer and Algorithm Organization" (eds D.J. Kuck, D.H. Lawrie, A.H. Sameh),,,Academic Press,New York,1977,207,228,Treats evaluation,1,0,

,20,0,0,0,0,0,von zur Gathen J,Panario D,,Factoring polynomials over finite fields,J. Symb. Comput.,31,,,2001,3,17,,1,0,

,20,0,0,0,0,0,von zur Gathen J,Shoup V,,Computing Frobenius maps and factoring polynomials,Comput. Complexity,2,,,1992,187,224,Method requires O((n²+nlogq)(logn)²loglogn) to factor a polynomial of degree n over F_q,1,0,

,20,0,0,0,0,0,Kaltofen E,Shoup V,,Fast polynomial factorization over high algebraic extensions of finite fields, in "Proc. 1997 Internat. Symp. Symbolic Alg. Comp.", W.W. Kuchlin ed,,,ACM Press,,1997,184,188,,1,0,

,20,0,0,0,0,0,Roelse P,,,Factoring high degree polynomials over F₂ with Niederreiter's algorithm on the IBM SP2,Math. Comp.,68,,,1999,868,880,Describes a computer program for parallel factorization over finite fields. Works on a poly of degree 3 000 000,1,0,

,2,4,7,17,0,0,Constantinides A,,,Applied Numerical Methods with Personal Computers,,,McGraw-Hill,New York,1987,0,0,Treats Newton, Graeffe, reguli falsi, evaluation,1,0,

,19,,0,0,0,0,Fagnano G.C.,,,Opere Matematiche,,,,Milano,1911,0,0,Deep treatment of low-degree,1,0,

,1,0,0,0,0,0,Eriksen O,Staunstrup J,,Concurrent algorithms for root searching,Acta Informatica,18-4,,,1983,361,376,Generalization of bisection,1,0,

,3,5,6,8,9,14,Baker C (ed.),Phillips C (ed),,The Numerical Solution of Nonlinear Problems,,,Clarendon Press,Oxford, England,1981,0,0,Treats Bernoulli, Bairstow, minimization, conditioning, Jenkins-Traub, Lehmer, simultaneous,1,0,

,10,0,0,0,0,0,Acosta D.J.,,,Newton's Rule of Signs for Imaginary Roots,Amer. Math. Monthly,110,,,2003,694,706,If Q_i = a_i²-a_i+1a_i-1 (i=1,…,n-1); Q_n = a_n²; Q₀ = a₀², then number of variations in sign in Q_n,…,Q₀ is a lower bound for the number of complex roots.,1,0,

,3,0,0,0,0,0,Yamamoto T.,Kanno S.,Atanassova L.,Validated Computation of Polynomial Zeros by the Durand-Kerner Method I and II, in " Topics in Validated Computations", ed J. Herzberger,,,Elsevier,Amsterdam,1994,27,62,,1,0,

,29,0,0,0,0,0,Thibaut G.,,,Mathematics in the Making in Ancient India.,,,Bagchi and Co.,Calcutta,1984,0,0,Early $\sqrt{2}$ ,1,0,

,2,0,0,0,0,0,Frontini M.,Sormani E.,,Some variants of Newton's method with third-order convergence,Appl. Math. Comput.,140,,,2003,419,426, $The efficiency is \sqrt[3]{3}$ ,1,0,

,19,29,0,0,0,0,Druxes J.,,,Ausfuhrlicher Lehrgang Arithmetik und Algebra nach modernen Grundsätzen,,,,Coln,1919,0,0,Treats square root, quadratic,1,0,

,11,0,0,0,0,0,Hinrichsen D,Pritchard A.J.,,On the robustness of root locations of polynomials under complex and real perturbations,Proc. 27th IEEE Conf. Dec. Control,,,,1988,1410,1414,,1,0,

,11,0,0,0,0,0,Kraus J,Anderson B.D.O.,Jury E.I. And Mansour M,On the robustness of low order Schur polynomials,IEEE Trans. Circ. Systems,35,,,1988,570,577,,1,0,

,24,,,,,,Jain M.K.,Inyengar S.R.K.,Jain R.K.,Numerical methods for scientific and engineering computations,,,Halstead,New York,1982,0,0,Treats bisection, Newton, Secant, Muller, Graeffe, Bairstow, convergence, acceleration,1,0,

,18,19,30,,,,Korn G.A.,Korn T.M.,,Mathematical handbook for scientists and engineers 2nd ed.,,,McGraw-Hill,New York,1968,0,0,Treats briefly Newton, Graeffe, QD, Secant, Muller, Sturm, Baistow, bounds, evaluation, and a matrix method,1,0,

,7,15,19,0,0,0,Pachner J,,,Handbook of numerical analysis applications,,,McGraw-Hill,New York,1984,0,0,Treats Secant, Laguerre, and low-degree,1,0,

,11,0,0,0,0,0,Soh C.B.,Berger C.S.,,Damping margins of polynomials with perturbed coefficients,IEEE Trans. Autom. Control,33,,,1988,509,511,Generalizes Kharitonov's theorem to sectors in complex plane,1,0,

,18,0,0,0,0,0,Diaz-Barrero, J.L.,,,Note on Bounds of the Zeros,Missouri J. Math. Sciences,14,,,2002,88,91,Bounds involve binomial coefficients and Fibonacci numbers,1,0,

,21,0,0,0,0,0,Pittaluga G.,Sacripante L.,,Bounds for the zeros of Hermite polynomials,Ann. Numer. Math.,21,,,1995,371,379,,1,0,

,3,0,0,0,0,0,Iliev, A.,Kyurkchiev, N.,,Generalization of Weierstrass-Dochev method for simultaneous extraction of only a part of all roots of algebraic polynomials: Part I.,C.R. Acad. Bulgare Sci.: Sci. Math. Nat.,55,,,2002,23,26,Title says it,1,0,

,11,0,0,0,0,0,Djaferis, T. J.,,,Shaping Conditions for the Robust Stability of Polynomials with Multilinear Parameter Uncertainty,Proc. 27th IEEE Conf. Dec. Contr.,,,,1988,526,531,,1,0,

,5,0,0,0,0,0,Kravanja P,Sakurai T,van Barel M,Error analysis of a derivative-free algorithm for computing zeros of holomorphic functions,Computing,70,,,2003,335,347,Uses quadrature,1,0,

,13,17,0,0,0,0,Pathan A,Collyer T,,The wonder of Horner's method,Math. Gaz.,87,,,2003,230,242,Evaluation and simple solution method,1,0,

,2,0,0,0,0,0,Frontini M,Sormani E,,Modified Newton's method with third-order convergence and multiple roots,J. Comput. Appl. Math.,156,,,2003,345,354,Uses approximate quadrature. For multiple roots convergence faster than classical Newton.,1,0,

,15,0,0,0,0,0,Kalantari B,Jin Y,,"On extraneous fixed-points of the Basic Family of iteration functions",BIT,43,,,2003,453,458,If a member of the Basic Family converges at all, it converges to a root.,1,0,

,7,0,0,0,0,0,Grau M,,,"An improvement to the computing of nonlinear equation solutions",Numer. Algs.,34,,,2003,1,12,Uses inverse (Hermite) interpolation,1,0,

,11,0,0,0,0,0,Soh C.B.,,,A simple geometrical proof of the box thereom,IMA J. Math. Control Inform.,7,,,1990,235,248,Generalizes Kharitonov's thereom,1,0,

,21,0,0,0,0,0,Calogero F,Perelomov A.M.,,"Asymptotic density of zeros of Hermite polynomials of diverging order and related properties of certain singular integral operators",Lett. Nuovo Cimento,23,,,1978,650,652,,1,0,

,11,0,0,0,0,0,Bose N.K.,,,A system-theoretic approach to the stability of sets of polynomials, in "Linear algebra and its role in system theory" ed. R.A. Brualdi et al,Amer. Math. Soc.,,,Providence R.I.,1985,25,34,,1,0,

,21,0,0,0,0,0,Davidson M.,,,Partition polynomials and their zeros,Analysis,21,,,2001,391,402,Coefficients all 0, +1, or -1.,1,0,

,13,0,0,0,0,0,Sakurai T,Sugiura H,,"On factorization of analytic functions and its verification",Reliable Comput.,6,,,2000,459,470,,1,0,

,13,0,0,0,0,0,Sakurai T,Sugiura H,,"Improvement of convergance of an iterative method for finding polynomial factors of analytic functions",J. Comput. Appl. Math.,40,,,2002,713,726,,1,0,

,19,0,0,0,0,0,Matthiessen,,,"Goniometrische Auflösung der algebraischen Gleichungen der ersten vier Grade mittels der Formel für die Tangente des vielfachen Winkels",Arch. Math. Phys. Ser 3,2,,,1902,109,110,Trigonometric treatment of low degree polynomials,1,0,

,21,0,0,0,0,0,Goh W.M.Y.,Wimp J,,"On the asymptotics of the Tricomi-Carlitz polynomials and their zero distributions",SIAM J. Math. Anal.,25,,,1994,420,428,,1,0,

,21,0,0,0,0,0,Nevai P,Van Assche W,,"Remarks on the (C, -1) summability of the distribution of zeros of orthogonal polynomials",Proc. Amer. Math. Soc.,122,,,1994,759,767,,1,0,

,21,0,0,0,0,0,Kuijlaars A.B.J.,Serra Capizzano S.,,"Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients",J. Approx. Theory,113,,,2001,142,155,,1,0,

,21,0,0,0,0,0,Reimer M,,,The main-roots of the Euler-Frobenius polynomials,J. Approx. Theory,45,,,1985,358,363,Considers largest root less than or equal to -1.,1,0,

,7,0,0,0,0,0,Richard F.K.,,,An improved Pegasus method for root finding,BIT,13,,,1973,423,427,Variation on reguli falsi with efficiency 1.642, about same as Muller,1,0,

,2,15,0,0,0,0,Lang M,Frenzel B,,Polynomial root finding,IEEE Signal Proc. Lett.,1,,,1994,141,143,Combines Muller and Newton method. Better than Jenkins-Traub or eigenvalue methods,1,0,

,2,4,16,10,0,0,John F,,,Lectures on Advanced Numerical Analysis,,,Gordon and Breach,New York,1966,0,0,Treats Newton, Sturm, Bemoulli, Graeffe,1,0,

,11,0,0,0,0,0,Anderson B.D.O.,Jury E.I.,Mansour M,On robust Hurwitz polynomials,IEEE Trans. Automat. Control,AC-32,,,1987,909,913,For n= 3,4,5 the number of polynomials needed to check robust stability is 1,2,3. For n greater than or equal to 6 it is 4.,1,0,

,13,0,0,0,0,0,Herzberger J,,,"Bounds for the R-order of certain iterative numerical processes",BIT,26,,,1986,259,262,,1,0,

,13,0,0,0,0,0,Herzberger J,,,"On the R-order of some recurrences with applications to inclusion methods",Computing,36,,,1986,175,180,,1,0,

,13,0,0,0,0,0,Kjurckchiev N,,,"Note on the estimation of the order of convergence of classes of iterative processes",BIT,32,,,1992,525,528,Relates to R-order,1,0,

,2,15,0,0,0,0,Petkovic, M.,Herceg, D.,,On rediscovered iteration methods for solving equations,J. Comput. Appl. Math.,107,,,1999,275,284,Shows that a class of iterative methods presented by Gerlach is equivalent to other well-known classes derived earlier.,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Zeros of polynomials and recurrence relations with periodic coefficients.,J. Comput. Appl. Math.,107,,,1999,241,255,Zeros of a famaily of polynomials defined by 3-term recurrence relations with periodic coefficients are evaluated with the help of Chebyshev polynomials.,1,0,

,2,7,15,21,0,0,Herzberger, J.,,,Bounds for the positive roots of a class of polynomials with applications.,BIT,39,,,1999,366,372,Solving problems of effective rate of an annuity leads to new bounds for the positive root of p(t) ≡ tⁿ-aΣ_ν=1ⁿ t^n-ν. The result also applies to the rate of convergence of interpolatory root-finding methods.,1,0,

,19,0,0,0,0,0,Nicholson, P.,,,A Practical System of Algebra,,,,London,1831,0,0,Method similar to Horner's.,1,0,

,13,0,0,0,0,0,Nicholson, P.,,,Essay on Involution and Evolution,,,Davis & Dickson,London,1831,0,0,Treats low-degree polynomials, and gives and ad hoc method for higher degree.,1,0,

,20,0,0,0,0,0,Lidl, R.,,,Computational Problems in the Theory of Finite Fields,Appl. Alg. Eng. Comm. Comp.,2,,,1991,81,89,Surveys methods of factorizing polynomials over finite fields, among other things.,1,0,

,20,0,0,0,0,0,Lenstra, H.W.,,,Algorithms for finite fields, in "Number Theory and Cryptography", Ed. J.H. Loxton,,,Cambridge Univ. Press,,1990,76,85,Discusses algorihms for factoring polynomials into irreducible factors.,1,0,

,19,0,0,0,0,0,Odstrcil, J.,,,New method of root calculation for quadratic equations,Casopis Pest. Mat. Fys.,7,,,0,102,113,,1,0,

,13,0,0,0,0,0,Bellavitis, G.,,,Di trovare le radici reali delle equazioni algebraische.,Mem. Ist. Ven. Sci. Let. Arti,3,,,1846,109,267,,1,0,

,19,20,0,0,0,0,Bellavitis, G.,,,Saggio sull'algebre degli imaginarii.,Mem. Ist. Ven. Sci. Let. Arti,4,,,1852,243,344,,1,0,

,19,0,0,0,0,0,Pavelle, R.,Wang, P.S.,,Macsyma from F to G,J. Symb. Comput.,1,,,1985,69,100,Polynomials up to quartic and some higher can be solved symbolically.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration d'un théorème fondamental de la théorie des équations algébriques.,C.R. Acad. Sci. Paris,96,,,1883,772,773,Proof of existence.,1,0,

,26,0,0,0,0,0,Wilkinson, J.,,,Modern error anlaysis,SIAM Rev.,13,,,1971,548,568,Less error in deflation if division done in order of increasing powers of x.Better still is a compromise between forward and backward division.,1,0,

,17,0,0,0,0,0,Reingold, E.M.,Srocks, A.I.,,Simple proofs of lower bounds for polynomial evaluation, in "Complexity of Computer Computations", Ed. R. Miller and J. Thatcher.,,,Plenum Press,New York,1972,21,30,An n'th degree polynomial can be evaluated in Floor(n/2)+2 multiplications and n adds/subs, if cost of preconditioning is not counted.,1,0,,p> ,17,0,0,0,0,0,Cormen, T.,Leiserson, C.,Rivest, R.,Introduction to Algorithms,,,MIT Press,,1990,0,0,Considers evaluation via the FFT.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Lobo, A.,,Factoring high-degree polynomials by the black box Berlekamp algorithm, in "Proc. Internat. Symp. On Symbolic and Algebraic Computation (ISSAC '94)" ed. J. Von Zur Gathen,,,ACM Press,New York,1994,90,98,Uses solution of structured linear systems over finite fields and matrix-vector multiplication.,1,0,

,17,0,0,0,0,0,Heintz, J.,,,On the computational complexity of polynomials, in "Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes", Ed. L. Huget and A. Poli,,,Springer-Verlag,New York,1989,269,300,For evaluation of d-degree polynomials, number of operations is at least Ceil(3d/2) (roughly). Gives examples of polynomials that are "hard to compute",1,0,

,20,29,0,0,0,0,Dickson, L.E.,,,History of the Theory of Numbers Vol. 1,,,Chelsea,New York,1952,215,215,Gives a method of solving x² = c(mod p) where p is a prime 4h+1 and some quadratic non-residue g of p is known.,1,0,

,15,0,0,0,0,0,Jovanovi&cacute, B.,,,A method for obtaining iterative formulas of higher order.,Mat. Vesnik,9,,,1972,365,369,Given an iterative method x_n+1 = φ(x_n) of order k, we derive another method of order at least k+1, I.e. x_n+1 =(x_n-φ(x_n))/(1-φ'(x_n)/k),1,0,

,2,15,29,0,0,0,Candela, V.,Marquina, A.,,Recurrence relations of rational cubic method II. The Chebyshev method.,Computing,45,,,1990,355,367,Compares Newton, Chebyshev and Halley methods for simple functions including n'th roots. The latter 2 methods are better.,1,0,

,26,0,0,0,0,0,Schätzle, R.,,,On the perturbation of the zeros of complex polynomials,IMA J. Numer. Anal.,20,,,2000,185,202,,1,0,

,1,2,7,24,0,0,Quarteroni, A.,Sacco, R.,Saleri, F.,Matematica Numerica,,,Springer-Verlag,New York,1998,0,0,Usual elementary treatment of Secant, Newton, Bisection, Muller, Aitken acceleration,1,0,

,2,0,0,0,0,0,Yang, Z.,,,Computing Equilibria and Fixed Points,,,Kluwer,Boston,1999,239,264,Considers Kuhn's algorithm, a kind of 2-dimensional bisection method,1,0,

,4,0,0,0,0,0,Mourrain, B.,Pan, V.Y.,,Lifting/Descending Processes for Polynomial Zeros,J. Complexity,16,,,2000,265,273,Uses Graeffe's method and Chebyshev-like lifting to factorize p(z) into F(z)G(z),1,0,

,1,0,0,0,0,0,Kavvadias, D.J.,Makri, F.S.,Vrahatis, M.N.,Locating and computing arbitrarily distributed zeros,SIAM J. Sci. Comput.,21,,,2000,954,969,Uses a generalized bisection method,1,0,

,2,0,0,0,0,0,Fouret, G.,,,Sur la Méthode d'Approximation de Newton,Nouv. Ann. Math,,,,1890,567,585,Gives a condition on f'(x) and f''(x) so that Newton's method converges,1,0,

,2,4,0,0,0,0,Gourdon, X.,,,Algorithmic Aspects of the Fundamental Theorem of Algebra,INRIA Report no. 1852,,,,1993,0,0,Combines Graeffe's and Newton's methods to factorize P into FG where F and G are about the same degree. Slower than Jenkins-Traub method but more robust on high degree polynomials.,1,0,

,29,0,0,0,0,0,Clark, W.E.,,,The Aryabhatiya of Aryabhata,,,Univ. Chicago Press,,1930,0,0,Gives a crude method for square and cube roots, dated about 500 A.D.,1,0,

,29,0,0,0,0,0,Kaye, G.R.,,,Indian Mathematics,,,,Calcutta,1915,0,0,Treats square and cube roots,1,0,

,19,0,0,0,0,0,Spearman, B.K.,Williams, K.S.,,Dihedral quintic polynomials and a theorem of Galois,Indian J. Pure Appl. Math.,30,,,1999,839,846,Given 2 roots, finds others as rational functions of them.,1,0,

,19,29,0,0,0,0,Gurjar, L.V.,,,Ancient Indian Mathematics and Vedha,,,,Poona,1947,0,0,Describes use of continued fractions for square root.,1,0,

,19,29,0,0,0,0,Bag, A.K.,,,Mathematics in Ancient and Medieval India,,,Chaukhambha Orientalia,,1979,0,0,Considers quadratics and square roots,1,0,

,20,0,0,0,0,0,Rosen, K.H.,,,Elementary Number Theory and its Applications,,,Addison-Wesley,Reading, Mass.,1984,0,0,Considers quadratic residues,1,0,

,10,0,0,0,0,0,Brunie, C.,Picart, P.S.,,A Fast Version of the Schur-Cohn Algorithm,J. Complexity,16,,,2000,54,69,Counts number of roots in unit disk of a polynomial of degree d. If bit size is σ, time complexity is of order d²σlog(dσ) loglog(dσ).log(d),1,0,

,20,0,0,0,0,0,Lange, T.,Winterhof, A.,,Factoring polynomials over arbitrary finite fields,Theoret. Comput. Sci.,234,,,2000,301,308,Factors most polynomials of degree n over F_q in order n^2+εlog²q operations,1,0,

,15,0,0,0,0,0,Kalantari, B.,Gerlach, J.,,Newton's method and generation of a determinantal family of iteration functions,J. Comput. Appl. Math.,116,,,2000,195,200,,1,0,

,27,0,0,0,0,0,Farahmand, K.,Hannigan, P.,,On the expected number of zero crossings of a random algebraic polynomial,Non-Lin Anal, Theory, Meths,Appls,30,,,1997,1219,1224,Number of zero crossings depends on ratio μ²/σ²,1,0,

,20,0,0,0,0,0,Tonelli, A.,,,Sulla risoluzione della congruenza x²≡c(mod p^λ),Atti R. Accad. Lincei, Rend. (Ser. 5),1,,,1892,116,120,,1,0,

,1,0,0,0,0,0,Favati, P. et al,,,An infinite precision bracketing algorithm with guaranteed convergence,Numerical Algorithms,20,,,1999,63,73,Convergence of the classical bisection method is not ensured when no information on the behaviour of the function is available. A modified bisection algorithm with guaranteed convergence is proposed and an upper bound to its compuational cost is given.,1,0,

,5,10,0,0,0,0,Brunetto, M.A.O.C.,Claudio, D.M.,Trevisan, V.,An Algebraic Algorithm to Isolate Complex Polynomial Zeros using Sturm Sequences,Comput. Math. Appl.,39(3),,,2000,95,105,Uses Sturm sequences and Argument Principle to enumerate zeros in a rectangle,1,0,

,31,0,0,0,0,0,Fergola, E.,,,Ricerce sulla risoluzione per Serie di Un'Equazione Qualunque,Ann. Mat. Pura Appl.,1,,,1858,0,0,,1,0,

,22,0,0,0,0,0,Alesina, A.,Galuzzi, M.,,Addendum to the Paper "A New proof of Vincent's Theorem",Enseign. Math. (Ser. 2),45,,,1999,379,380,Their proof is different from Ostrowski's,1,0,

,22,0,0,0,0,0,Ostrowski, A.M.,,,Note on Vincent's theorem,Ann. Math. Ser. 2,52,,,1950,702,707,Improves upon a result of Uspensky concerning a bound related to Vincent's method,1,0,

,18,0,0,0,0,0,Mignotte, M.,Cerlienco, L.,Piras, F.,Computing the measure of a polynomial,J. Symb. Comput.,4,,,1987,21,23,Finds bounds on roots and number outside unit circle,1,0,

,2,0,0,0,0,0,Peitgen, H.O.,Richter, P.H.,,The beauty of fractals,,,Springer-Verlag,Berlin,1986,0,0,Considers regions of convergence of Newton's method,1,0,

,19,0,0,0,0,0,Sarton, G.,,,Six Wings: Men of Science in the Renaissance,,,Indiana Univ. Press,Bloomington,1957,0,0,Good history of Cardan, etc.,1,0,

,19,0,0,0,0,0,Wightman, W.P.D.,,,Science and the Renaissance Vol. 1,,,Oliver & Boyd,Edinburgh,1962,0,0,Historical approach to low order equations,1,0,

,19,0,0,0,0,0,Bhaskara,,,Siddhanta Siromani,,,,,1150,0,0,,1,0,

,17,0,0,0,0,0,Rabin, M.O.,Winograd, S.,,Fast Evaluation of Polynomials by Rational Preparation,Comm. Pure Appl. Math.,25,,,1972,433,458,With pre-conditioning, can evaluate in 1/n + O(log n) multiplies and ~n adds.,1,0,

,17,0,0,0,0,0,Revah, L.,,,On the number of multiplications/ divisions evaluating a polynomial with auxiliary functions.,SIAM J. Comput.,4,,,1975,381,392,For n < 9, minimum number is ceil[(n+2)/2]. For n>=9, it is almost always ceil[(n+1)/2].,1,0,

,7,0,0,0,0,0,Opitz, G.,,,Zum Vergleich von iterationsverfahren zur Gleichungsauflösung,Z. Angew. Math. Mech. (T),41,,,1961,48,50,Uses divided difference interpolation over several previous iterations,1,0,

,7,0,0,0,0,0,Opitz, G.,,,Gleichungsauflösung mittels einer speziellen Interpolation,Z. Angew. Math. Mech.,38,,,1958,276,277,Uses divided difference interpolation over several previous iterations,1,0,

,16,0,0,0,0,0,Kjurkchiev, N.,Herzberger, J.,,On some bounds for polynomial roots obtained when determining the R-order of iterative processes.,Serdica,19,,,1993,53,58,Order of convergence is bounded below by the unique positive root of a certain polynomial. We show some new e