并行求解线性方程组的非定常二级多分裂迭代方法  

Non Stationary Two Stage Multisplitting Iterative Methods for the Parallel Solutions of Linear Systems

作　　者：谷同祥[1,2] 王能超[1,2] 

机构地区：[1]河南师范大学数学系 [2]华中理工大学并行计算研究所

出　　处：《工程数学学报》1997年第4期25-32,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金

摘　　要：提出了并行求解线性方程组的非定常二级多分裂迭代方法（简称ＮＳＴＳＭ方法），方法中内代数ｓ（ｉ）可随ｉ而变化，其中ｉ表示第ｉ步外迭代；给出了保证对任意ｓ（ｉ）≥１，ｉ＝１，２，…，方法均收敛的关于分裂的条件；进一步研究了系数矩阵为Ｈ矩阵时（此时不要求是单调的），方法的收敛性。数值例子表明：ＮＳＴＳＭ方法是有效的。In this paper, we propose non stationary two stage multisplitting iterative method for the parallel solutions of linear systems (we take it NSTSM method in brief), in which the number of inner iteration s(i) changes with i, the outer iteration index. Conditions on the splitting are given so that the method is convergent for any s(i)≥1. Convergence is fruther studied for splittings of H matrices, which are not necessarily monotone. Numerical examples are presented to illustrat the effectiveness of NSTSM method.

关 键 词：线性代数方程组 并行算法 迭代法 多分裂迭代法 

分 类 号：O241.6[理学—计算数学]