Some convergence conditions for a class of parallel decomposition-type linear relaxation methods

Abstract

A class of multi-parameter relaxed parallel decomposition methods, called parallel decomposition-type unsymmetric AOR (Accelerated Overrelaxation) methods, for solving large sparse systems of linear equations on SIMD multiprocessor systems has been proposed by Zhong-Zhi Bai. When the coefficient matrix of the linear system is a (block) H-matrix, some sufficient conditions for the convergence of these methods have been proved by the same author. For the same class of linear systems some new convergence conditions, allowing us to improve the known convergence area, will be established in this paper.