On parallel multisplitting iterative methods for singular linear systems
type: Item
instance of: scholarly article
title: On parallel multisplitting iterative methods for singular linear systems
zbMATH Open document ID: 1069.65029
published in: Applied Mathematics and Computation
publication date: 2005-02-23T00:00:00Z
review text: The author considers the semiconvergence [cf. \textit{J. P. Kavanagh} and \textit{M. Neumann}, SIAM J. Matrix Anal. Appl. 10, 210--218 (1989; Zbl 0676.65025)] of parallel multisplitting iterative methods [cf. \textit{D. P. O'Leary} and \textit{R. C. White}, SIAM J. Alg. Disc. Methods 6, 630--640 (1985; Zbl 0582.65018)] and extrapolated parallel methods [cf. \textit{A. Frommer} and \textit{G. Mayer}, Linear Algebra Appl. 119, 141--152 (1989; Zbl 0676.65022)] for finding solutions to singular solvable systems of linear equations. After some preliminary definitions and facts, three main cases: \(P\)-regular, sub-regular and nonnegative multisplittings are investigated. Related lemmas and theorems are stated and proved. The final section contains theorems concerning conditions for the semiconvergence of parallel generalized accelerated overrelaxation (GAOR), block AOR (BAOR), AOR, parallel generalized successive overrelaxation (GSOR), block SOR (BSOR), SOR, extrapolated parallel (generalized, block) AOR and extrapolated parallel (general, block) SOR methods which are simple conclusions for the results proved in previous sections.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 2137707
zbMATH Keywords: singular linear systems
zbMATH Keywords: parallel multisplitting iterative methods
zbMATH Keywords: semiconvergence
zbMATH Keywords: accelerated overrelaxation
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: extrapolation
author: Yongzhong Song
reviewed by: Przemysław Stpiczyński
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.120
OpenAlex ID: W1983128947
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DOI: 10.1016/J.AMC.2003.12.120
description: scientific article; zbMATH DE number 2137707