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Mathematics of Computation

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Matrix representations of nonlinear equation iterations--Application to parallel computation

Author: John R. Rice
Journal: Math. Comp. 25 (1971), 639-647
MSC: Primary 65H05
MathSciNet review: 0303714
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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 [Enhancements On Off] (What's this?)

  • [1] A. Feldstein & R. M. Firestone, ``A study of Ostrowski efficiency for composite iteration algorithms,'' Proc. Nat. Conf. Assoc. Comp. Mach., 1969, pp. 147-155.
  • [2] W. L. Miranker, ``Parallel methods for approximating the root of a function,'' IBM J. Res. Develop., v. 13, 1969, pp. 297-301. MR 39 #1109. MR 0239752 (39:1109)
  • [3] G. S. Shedler, ``Parallel numerical methods for the solution of equations,'' Comm. ACM, v. 10, 1967, pp. 286-291. MR 39 #2321. MR 0240976 (39:2321)
  • [4] SIGNUM Newsletter, v. 2, 1967, no. 3.

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Keywords: Nonlinear equations, parallel computation, iteration, matrix representations, convergence order
Article copyright: © Copyright 1971 American Mathematical Society

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