H-矩阵线性方程组的一类预条件并行多分裂SOR迭代法

A Class of Preconditioned Parallel Multi-Splitting SOR Iteration Methods for H-Matrix Linear Systems

基于并行多分裂算法的思想及SOR迭代格式,本文提出一种求解H-矩阵线性方程组新的并行多分裂SOR迭代法,新方法某种程度上避免了SOR迭代法中选取最优参数的困难.同时,选取Kohno等(1997)提出的预条件子P=I+S_α对原始线性方程组进行预处理,进而给出了一种实用的预条件并行多分裂SOR迭代法.理论分析和数值实验均表明,新算法是实用而有效的.

Based on the idea of parallel multi-splitting and SOR iteration scheme,a class of parallel multi-splitting SOR iteration method is proposed in this paper.It avoids the difficulty of selecting the optimal parameters in SOR iteration method partially.Moreover,the original systems is improved by using the preconditioner P=I+S_αpresented by Kohno et al.(1997),and then a practical preconditioned parallel multi-splitting SOR iteration method is given.Theoretical analysis and numerical results show that the proposed algorithms are practical and efficient.