The relationship between the Jacobi and the successive overrelaxation (SOR) matrices of a k-cyclic matrix
type: Item
instance of: scholarly article
title: The relationship between the Jacobi and the successive overrelaxation (SOR) matrices of a k-cyclic matrix
zbMATH Open document ID: 0676.65020
DOI: 10.1016/0898-1221(89)90018-7
author: S. Galanis
author: A. Hadjidimos
author: Dimitrios Noutsos
publication date: 1989-01-01T00:00:00Z
review text: In the SOR theory [cf. e.g. \textit{D. Young}, Iterative solution of large linear systems (1971; Zbl 0231.65034)] the relation \([\lambda +\omega - 1]^ k=\omega^ k\mu^ k\lambda^{k-1}\) between the eigenvalues of the Jacobi and the SOR matrix \(\mu\), \(\lambda\) and the relaxation parameter \(\omega\) play an important role. The authors show that for a certain subclass of consistently ordered matrices the same relation is true for the iteration matrices. This implies that the SOR method in this case is equivalent to a monoparametric k-step iterative method in the sense of \textit{W. Niethammer} and \textit{D. S. Varga} [Numer. Math. 41, 177- 206 (1983; Zbl 0487.65018)].
reviewed by: G.Maeß
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4108010
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: Jacobi matrix
zbMATH Keywords: SOR matrix
zbMATH Keywords: relaxation parameter
zbMATH Keywords: consistently ordered matrices
zbMATH Keywords: iteration matrices
zbMATH Keywords: k-step iterative method
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90018-7
OpenAlex ID: W2004944273
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4108010