Convergence analysis of preconditioned AOR iterative method for linear systems
type: Item
instance of: scholarly article
title: Convergence analysis of preconditioned AOR iterative method for linear systems
zbMATH Open document ID: 1198.65061
DOI: 10.1155/2010/341982
published in: Mathematical Problems in Engineering
publication date: 2010-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/225348
review text: Summary: \(M\)-(\(H\)-)matrices appear in many areas of science and engineering, for example, in the solution of the linear complementarity problem (LCP) in optimization theory and in the solution of large systems for real-time changes of data in fluid analysis in car industry. Classical (stationary) iterative methods used for the solution of linear systems have been shown to convergence for this class of matrices. In this paper, we present some comparison theorems on the preconditioned accelerated overrelaxation (AOR) iterative method for solving the linear system. Comparison results show that the rate of convergence of the preconditioned iterative method is faster than the rate of convergence of the classical iterative method. Meanwhile, we apply the preconditioner to \(H\)-matrices and obtain the convergence result. Numerical examples are given to illustrate our results.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 5793738
zbMATH Keywords: preconditioning
zbMATH Keywords: \(M\)-matrices
zbMATH Keywords: linear complementarity problem
zbMATH Keywords: comparison theorems
zbMATH Keywords: accelerated overrelaxation (AOR) iterative method
zbMATH Keywords: \(H\)-matrices
zbMATH Keywords: convergence result
zbMATH Keywords: numerical examples
Wikidata QID: Q58653021
author: Qingbing Liu
author: Guoliang Chen
MaRDI profile type: Publication
OpenAlex ID: W2052033075
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description: scientific article; zbMATH DE number 5793738