Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 341982, 14 pages
doi:10.1155/2010/341982
Research Article

Convergence Analysis of Preconditioned AOR Iterative Method for Linear Systems

Qingbing Liu1,2 and Guoliang Chen2

1Department of Mathematics, Zhejiang Wanli University, Ningbo 315100, China
2Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 26 June 2009; Revised 21 February 2010; Accepted 13 May 2010

Academic Editor: Paulo Batista Gonçalves

Copyright © 2010 Qingbing Liu and Guoliang Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 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.