Sequential and parallel synchronous alternating iterative methods

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Title: Sequential and parallel synchronous alternating iterative methods
Authors: Climent, Joan-Josep | Perea Marco, Mari Carmen | Tortosa, Leandro | Zamora, Antonio
Research Group/s: Criptología y Seguridad Computacional
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad de Alicante. Departamento de Ciencia de la Computación e Inteligencia Artificial
Keywords: Nonsingular matrix | Iterative method | Spectral radius | Splitting | Multisplitting | Alternating method | Stationary method | Nonstationary method | Convergence conditions | Comparison conditions
Knowledge Area: Álgebra | Ciencia de la Computación e Inteligencia Artificial
Issue Date: 24-Nov-2003
Publisher: American Mathematical Society
Citation: CLIMENT, Joan-Josep, et al. “Sequential and parallel synchronous alternating iterative methods”. Mathematics of Computation. Vol. 73, No. 246 (2003). ISSN 0025-5718, pp. 691-717
Abstract: The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.
URI: http://hdl.handle.net/10045/25282
ISSN: 0025-5718 (Print) | 1088-6842 (Online)
DOI: 10.1090/S0025-5718-03-01607-7
Language: eng
Type: info:eu-repo/semantics/article
Rights: First published in Math. Comp. 73 (2004), published by the American Mathematical Society.
Peer Review: si
Publisher version: http://dx.doi.org/10.1090/S0025-5718-03-01607-7
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