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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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 | References | Similar Articles | Additional Information

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. 13 (1969), 297–301. MR 0239752 (39 #1109)
  • [3] G. S. Shedler, Parallel numerical methods for the solution of equations, Comm. ACM 10 (1967), 286–291. MR 0240976 (39 #2321)
  • [4] SIGNUM Newsletter, v. 2, 1967, no. 3.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0303714-7
PII: S 0025-5718(1971)0303714-7
Keywords: Nonlinear equations, parallel computation, iteration, matrix representations, convergence order
Article copyright: © Copyright 1971 American Mathematical Society