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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Matrix representations of nonlinear equation iterations—Application to parallel computation
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by John R. Rice PDF
Math. Comp. 25 (1971), 639-647 Request permission

Abstract:

A matrix representation of iterative methods is presented which includes almost all those based on polynomial methods. A simple lemma and corollaries are established which show that the order of convergence of the iteration is the spectral radius of the matrix representation. A number of old and new methods, particularly those adapted to parallel computation, are analyzed using this representation.
References
    A. Feldstein & R. M. Firestone, “A study of Ostrowski efficiency for composite iteration algorithms,” Proc. Nat. Conf. Assoc. Comp. Mach., 1969, pp. 147-155.
  • W. L. Miranker, Parallel methods for approximating the root of a function, IBM J. Res. Develop. 13 (1969), 297–301. MR 239752, DOI 10.1147/rd.133.0297
  • G. S. Shedler, Parallel numerical methods for the solution of equations, Comm. ACM 10 (1967), 286–291. MR 0240976, DOI 10.1145/363282.363301
  • SIGNUM Newsletter, v. 2, 1967, no. 3.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 639-647
  • MSC: Primary 65H05
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0303714-7
  • MathSciNet review: 0303714