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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


A class of globally convergent iteration functions for the solution of polynomial equations
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by J. F. Traub PDF
Math. Comp. 20 (1966), 113-138 Request permission
  • Enzo Aparo, Applicazione di un nuovo metodo per la risoluzione numerica delle equazioni algebriche, Bol. Soc. Portuguesa Mat. Ser. A 1 (1948), 49–57 (Italian). MR 25260
  • Enzo Aparo, Un procedimento iterativo per la risoluzione numerica delle equazioni algebriche, Ricerca Sci. 24 (1954), 1003–1005 (Italian). MR 61885
  • F. L. Bauer, "Beiträge zur Entwicklung numerischer Verfahren für programmgesteuerte Rechenanlagen. a) I. "Quadratisch konvergente Durchführung der Bernoulli-Jacobischen Methode zur Nullstellenbestimmung von Polynomen," S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., v. 1954, 1955, pp. 275–303. MR 18, 151. b) II. Direkte Faktorisierung eines Polynoms, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. v. 1956, 1957, pp. 163–203. MR 19, 686.
  • Friedrich L. Bauer, Das Verfahren der abgekürzten Iteration für algebraische Eigenwertprobleme, insbesondere zur Nullstellenbestimmung eines Polynoms, Z. Angew. Math. Phys. 7 (1956), 17–32 (German). MR 79835, DOI 10.1007/BF01600724
  • D. Bernoulli, "Observationes de Seriebus," Comment. Acad. Sc. Petrop., v. 3, 1728, pp. 85–100.
  • Fritz Cohn, Ueber die in recurrirender Weise gebildeten Grössen und ihren Zusammenhang mit den algebraischen Gleichungen, Math. Ann. 44 (1894), no. 4, 473–538 (German). MR 1510849, DOI 10.1007/BF01446677
  • L. E. Dickson, New First Course in the Theory of Equations, Wiley, New York, 1939. MR 1, 1. L. Euler, "De usu serierum recurrentium in radicibus aequationum indagandis," Opera Omnia, Ser. 1, v. 8, pp. 339–361.
  • Thornton C. Fry, Some numerical methods for locating roots of polynomials, Quart. Appl. Math. 3 (1945), 89–105. MR 12910, DOI 10.1090/S0033-569X-1945-12910-1
  • E. Furstenau, Darstellung der reelen Wurzeln algebraischer Gleichungen durch determinanten der Coefficienten, Marburg, 1860. E. Furstenau, Neue Methode zur Darstellung und Berechnung der imaginären Wurzeln algebraischen Gleichungen, Marburg, 1867.
  • H. J. Hamilton, A type of variation on Newton’s method, Amer. Math. Monthly 57 (1950), 517–522. MR 39367, DOI 10.2307/2307934
  • Alston S. Householder, Principles of numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059056
  • Julius König, Ueber eine Eigenschaft der Potenzreihen, Math. Ann. 23 (1884), no. 3, 447–449 (German). MR 1510264, DOI 10.1007/BF01446400
  • Stephen Kulik, A method for approximating the zeros of analytic functions, Duke Math. J. 24 (1957), 137–141. MR 86865
  • Stephen Kulik, On the solution of algebraic equations, Proc. Amer. Math. Soc. 10 (1959), 185–192. MR 107363, DOI 10.1090/S0002-9939-1959-0107363-1
  • Luigi Pepe, Three “first editions” and an unpublished introduction to Lagrange’s Théorie des fonctions analytiques, Boll. Storia Sci. Mat. 6 (1986), no. 1, 17–44 (Italian). MR 876555
  • F. Meyer, "Zur Auflösung der Gleichungen," Math. Ann., v. 33, 1880, pp. 511–524.
  • W. D. Munro, Some iterative methods for determining zeros of functions of a complex variable, Pacific J. Math. 9 (1959), 555–566. MR 107364
  • C. Runge, Entwicklung der Wurzeln, Acta Math. 6 (1885), no. 1, 305–318 (German). Einer Algebraischen Gleichung in Summen von Rationalen Functionen der Coefficienten. MR 1554667, DOI 10.1007/BF02400419
  • E. Schröder, "Über unendlich viele Algorithmen zur Auflösung der Gleichungen," Math. Ann., v. 2, 1870, pp. 317–365. J. Sebastiäo e Silva, "Sur une méthode d’approximation semblable à celle de Gräffe," Portugal. Math., v. 2, 1941, pp. 271–279. MR 3, 235. T. Simpson, Treatise of Algebra, 5th Edition, London, 1782.
  • J. F. Traub, Iterative methods for the solution of equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0169356
  • J. F. Traub, On Lagrange-Hermite interpolation, J. Soc. Indust. Appl. Math. 12 (1964), 886–891. MR 172443
  • J. F. Traub, Generalized sequences with applications to the discrete calculus, Math. Comp. 19 (1965), 177–200. MR 179489, DOI 10.1090/S0025-5718-1965-0179489-9
  • J. F. Traub, Solution of linear difference and differential equations, Bull. Amer. Math. Soc. 71 (1965), 538–541. MR 174881, DOI 10.1090/S0002-9904-1965-11320-9
  • J. F. Traub, Associated polynomials and the solution of linear problems. (To appear.) E. T. Whittaker, "A formula for the solution of algebraic or transcendental equations," Proc. Edinburgh Math. Soc., v. 36, 1918, pp. 103–106.
  • A. Zajta, Untersuchungen über die Verallgemeinerungen der Newton-Raphsonschen Wurzelapproximation, Acta Tech. Acad. Sci. Hungar. 15 (1956), 233–260 (German, with English, French and Russian summaries). MR 81527
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Additional Information
  • © Copyright 1966 American Mathematical Society
  • Journal: Math. Comp. 20 (1966), 113-138
  • MSC: Primary 65.50
  • DOI:
  • MathSciNet review: 0192655