Matrix representations of nonlinear equation iterations—Application to parallel computation
HTML articles powered by AMS MathViewer
- 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.
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