病态线性方程组的一类迭代改进法  

A Class of Iterative Modification Method for Ill-conditioned Linear Systems

作　　者：关晋瑞[1] 温瑞萍[1] GUAN Jinrui;WEN Ruiping(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《湖北民族大学学报（自然科学版）》2020年第3期290-292,312,共4页Journal of Hubei Minzu University:Natural Science Edition

基　　金：山西省高等学校科技创新项目(2019L0783);山西省应用基础研究计划项目(201901D211423).

摘　　要：本文研究了病态线性方程组的求解问题.基于系数矩阵的位移分裂,提出了一类迭代法以计算原方程组的解,证明了当系数矩阵为正稳定矩阵时所提出的迭代法是绝对收敛的.理论分析和数值实验表明,新方法是可行的,而且在一定情况下可以求得原方程组的较为精确的解.In this paper,we consider the problem of solving ill-conditioned linear systems.Based on the displacement splitting of the coefficient matrix,a kind of iterative method is proposed to compute the solution of the original equations,and it is proved that the iterative method is absolutely convergent when the coefficient matrix is a positive stable matrix.Theoretical analysis and numerical experiments show that the new iterative method is feasible and can obtain more accurate solution of the original equations under certain conditions.

关 键 词：病态线性方程组 条件数 正稳定矩阵 迭代法 

分 类 号：O241.6[理学—计算数学]