Models of parallel chaotic iteration methods
type: Item
instance of: scholarly article
title: Models of parallel chaotic iteration methods
zbMATH Open document ID: 0645.65018
DOI: 10.1016/0024-3795(88)90227-3
author: R. Bru
author: Ludwig Elsner
author: M. Neumann
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://pub.uni-bielefeld.de/record/1780549
review text: Linear systems \(Ax=b\) where the matrix is monotonic i.e. has a nonnegative inverse are considered. The convergence of parallel algorithms, where each processor performs several iterations updating a part of x between each global update of the whole of x, is studied and proved in two cases. Both the free steering method of \textit{A. M. Ostrowski} [J. Math. Anal. Appl. 2, 351-369 (1961; Zbl 0100.333)], and the chaotic relaxation by \textit{D. Chazan} and \textit{W. Miranker} [Linear Algebra Appl. 2, 199-222 (1969; Zbl 0225.65043)] as well as the block Jacobi iteration are covered by the theory.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4052887
zbMATH Keywords: nonnegative inverse
zbMATH Keywords: convergence
zbMATH Keywords: parallel algorithms
zbMATH Keywords: free steering method
zbMATH Keywords: chaotic relaxation
zbMATH Keywords: block Jacobi iteration
reviewed by: Axel Ruhe
MaRDI profile type: Publication
OpenAlex ID: W1971296985
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description: scientific article; zbMATH DE number 4052887