On the semiconvergence of extrapolated iterative methods for singular linear systems
type: Item
instance of: scholarly article
title: On the semiconvergence of extrapolated iterative methods for singular linear systems
zbMATH Open document ID: 1027.65040
DOI: 10.1016/S0168-9274(02)00168-X
author: Yongzhong Song
author: Li Wang
published in: Applied Numerical Mathematics
publication date: 2003-03-10T00:00:00Z
review text: The solution of square linear systems with singular coefficient matrix by extrapolated iterative methods is considered. Sufficient and necessary conditions for the semiconvergence of the extrapolated iterative methods are presented, extending the extrapolation theorem given by \textit{Z. Cao} [Appl. Numer. Anal. 27, 203-209 (1998; Zbl 0927.65052)] and improving the corresponding results by \textit{Y. Song} [J. Comput. Appl. Math. 106, 117-129 (1999; Zbl 0930.65033)]. In particular, the semiconvergence of the (generalized, block) Jacobi-overrelaxation (JOR) and (generalized, block) accelerated overrelaxation (AOR) methods are investigated. Five examples illustrate and show the limits of the theoretical results.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1879017
zbMATH Keywords: singular system
zbMATH Keywords: extrapolated iterative method
zbMATH Keywords: AOR method
zbMATH Keywords: JOR method
zbMATH Keywords: semiconvergence
zbMATH Keywords: numerical examples
zbMATH Keywords: Jacobi-overrelaxation
zbMATH Keywords: acceleration overrelaxation
reviewed by: René Lamour
MaRDI profile type: Publication
cites work: Q3943082
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full work available at URL: s0168-9274(02)00168-x
OpenAlex ID: W2020795305
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description: scientific article; zbMATH DE number 1879017