M-矩阵Sylvester方程的一类Smith-like迭代法  

A CLASS OF SMITH-LIKE ITERATION METHOD FOR M-MATRIX SYLVESTER EQUATIONS

作　　者：关晋瑞 王志欣 任孚鲛[1] GUAN Jin-rui;WANG Zhi-xin;REN Fu-jiao(School of Mathematics and Statistics,Taiyuan Normal University,Shanxi 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《数学杂志》2023年第5期389-397,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China (12001395);Natural Science Foundation of Shanxi province (201901D211423)。

摘　　要：本文研究了M-矩阵Sylvester方程的数值解法,这类矩阵方程广泛出现在科学计算和工程应用的许多领域.利用M-矩阵的性质和Smith方法的思想,提出了一类Smith-like迭代法以求解M-矩阵Sylvester方程,并给出了新方法的收敛性分析.数值实验表明,新方法是可行的,而且在一定条件下也是较为有效的.This paper considers numerical methods for solving M-matrix Sylvester equations,which are widely encountered in many fields of scientific computing and engineering applications.Based on the properties of M-matrix and the idea of Smith method,a class of Smith-like iteration method is proposed to solve M-matrix Sylvester equations,and convergence analysis of the new method is given.Numerical experiments show that the proposed method is feasible and is effective under certain conditions.

关 键 词：SYLVESTER方程 M-矩阵 Smith方法 

分 类 号：O241.6[理学—计算数学]