求解多右端对称线性方程组的一种极小向后扰动块方法  

A Minimum Backward Perturbation Block Method for Symmetric Linear Systems with Multiple Right-hand Sides

作　　者：朱景福 李欣 郭东山 ZHU Jingfu;LI Xin;GUO Dongshan(College of Science,Guangdong University of Petrochemical Technology,Maoming 525000,China)

机构地区：[1]广东石油化工学院理学院,广东茂名525000

出　　处：《广东石油化工学院学报》2022年第4期70-73,78,共5页Journal of Guangdong University of Petrochemical Technology

基　　金：广东石油化工学院人才引进启动项目(2018rc44,2018rc45)。

摘　　要：文章研究求解多右端对称线性方程组AX=B的数值方法,考虑在利用块Lanczos方法求解多右端对称线性方程组的过程中,采用极小向后扰动范数作为算法终止的判定条件,提出求解多右端对称线性方程组的极小向后扰动块Lanczos方法,并通过理论分析和数值实验讨论了算法的有效性。In this paper,numerical method for symmetric linear systems AX=B with multiple right-hand sides is studied.Considering that the minimum backward perturbation norm is used as the judgment condition for the termination of the algorithm in the process of using the block Lanczos method to solve the multiple right-hand symmetric linear systems,the minimum backward perturbation block Lanczos method for solving the multiple right-hand symmetric linear systems is proposed,and the effectiveness of the algorithm is discussed through theoretical analysis and numerical experiments.

关 键 词：KRYLOV子空间 多右端 块Lanczos过程 极小向后扰动 

分 类 号：O242.2[理学—计算数学]