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

作　　者：温瑞萍[1] 段辉[2] WEN Ruiping;DUAN Hui(Laboratory of Engineering&Computing Science,Shanxi Provincial Department of Education/Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China;Department of Computer Science and Technology,Lvliang University,Lvliang 033000,China)

机构地区：[1]太原师范学院工程科学计算省高校重点实验室/数学系,山西晋中030619 [2]吕梁学院计算机科学与技术系,山西吕梁033000

出　　处：《应用数学》2020年第4期814-825,共12页Mathematica Applicata

基　　金：国家自然科学基金(11371275);山西省自然科学基金(201901D211423);山西省高等学校科学研究优秀成果培育项目资助(2019KJ035)。

摘　　要：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.

关 键 词：H-矩阵 预处理 并行多分裂 SOR迭代法 

分 类 号：O241.6[理学—计算数学]