On the exact \(p\)-cyclic SSOR convergence domains
type: Item
instance of: scholarly article
title: On the exact \(p\)-cyclic SSOR convergence domains
zbMATH Open document ID: 0840.65020
DOI: 10.1016/0024-3795(94)00048-4
published in: Linear Algebra and its Applications
publication date: 1996-06-30T00:00:00Z
review text: This paper considers convergence domains for symmetric successive overrelaxation (SSOR) applied to a block \(p\)-cyclic, consistently ordered matrix \(A \in \mathbb{C}^{n,n}\). If \(B\) is the block Jacobi matrix and \(S_\omega\) the block SSOR matrix associated with \(A\), \textit{A. Hadjidimos} and \textit{M. Neumann} [J. Comput. Appl. Math. 33, No. 1, 35-52 (1990; Zbl 0716.65027)] derived in the \((\rho(|B|), \omega)\) plane convergence domains associated with \(p\)-cyclic, consistently ordered matrices for any order \(p \geq 3\). The current authors further assume that the eigenvalues of \(B^p\) are real and one-signed and show how to derive exact convergence domains in the \((\rho(B), \omega)\) plane in both the nonnegative and nonpositve cases for all \(p \geq 3\).
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 841762
zbMATH Keywords: convergence domains
zbMATH Keywords: symmetric successive overrelaxation
zbMATH Keywords: block \(p\)-cyclic, consistently ordered matrix
author: A. Hadjidimos
author: Dimitrios Noutsos
author: M. Tzoumas
reviewed by: Adrian Swift
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00048-4
OpenAlex ID: W1980804981
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description: scientific article; zbMATH DE number 841762