Optimum first and second order extrapolations of successive overrelaxation type methods for certain classes of matrices
type: Item
instance of: scholarly article
title: Optimum first and second order extrapolations of successive overrelaxation type methods for certain classes of matrices
zbMATH Open document ID: 0683.65019
DOI: 10.1007/BF02219233
author: S. Galanis
author: A. Hadjidimos
author: Dimitrios Noutsos
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: Sei A eine quadratische, 2-zyklische und konsistent geordnete Matrix. Die Quadrate der Eigenwerte der zu A gehörigen Jakobi-Matrix mögen auf der Strecke \(S_{\phi}=\{z:\) \(z=re^{i\phi}\), \(0\leq \mu^ 2<r\leq {\bar \mu}^ 2\}\) mit \(1\not\in S_{\phi}\) liegen. Es werden zu verschiedenen von Parametern abhängigen Iterationsverfahren zur Lösung von \(Ax=b\) optimale Parameter bestimmt. Dabei werden manchmal ein Parameter ``gut'' und nur die anderen optimal gewählt.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4119487
zbMATH Keywords: weakly 2-cyclic consistently ordered
zbMATH Keywords: optimum successive overrelaxation
zbMATH Keywords: second order extrapolation
zbMATH Keywords: Gauss-Seidel method
zbMATH Keywords: comparison
zbMATH Keywords: asymptotic convergence factors
MaRDI profile type: Publication
cites work: On the optimization of a class of second order iterative schemes
cites work: Optimum Accelerated Overrelaxation Method in a Special Case
cites work: Optimum second order stationary extrapolated iterative schemes
cites work: Q3943082
cites work: Convergence of block iterative methods applied to sparse least-squares problems
cites work: The optimal solution to the problem of complex extrapolation of a first- order scheme
cites work: Optimum sor methods for a class of linear systems
cites work: A survey of the iterative methods for the solution of linear systems by extrapolation, relaxation and other techniques
cites work: Q3909906
cites work: Extrapolated accelerated gauss-seidel methods
cites work: On complex successive overrelaxation
cites work: The Tchebychev iteration for nonsymmetric linear systems
cites work: Optimal Parameters for Linear Second-Degree Stationary Iterative Methods
cites work: Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems
cites work: Iterationsverfahren und allgemeine Euler-Verfahren. (Iterative and general Euler methods)
cites work: The analysis of k-step iterative methods for linear systems from summability theory
cites work: Richardson's iteration for nonsymmetric matrices
cites work: Q5342712
cites work: Iterative Methods for Solving Partial Difference Equations of Elliptic Type
cites work: Q5639278
description: scientific article; zbMATH DE number 4119487