M-矩阵Sylvester方程的一类交替方向迭代法  

A class of alternating direction iterative method for M-matrix Sylvester equations

作　　者：关晋瑞 任孚鲛[1] GUAN Jinrui;REN Fujiao(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 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：《纯粹数学与应用数学》2024年第2期347-356,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(12001395);山西省自然科学基金(201901D211423)。

摘　　要：Sylvester方程广泛出现在科学计算和工程应用的许多领域中,本文研究了M-矩阵Sylvester方程的数值解法.基于M-矩阵的性质和交替方向迭代的思想,提出了一类交替方向迭代法以求解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.Sylvester equation is widely used in many fields of scientific computing and engineering applications. In this paper, numerical methods for solving M-matrix Sylvester equation are discussed.Based on the properties of M-matrix and the idea of alternating direction iteration, a class of alternating direction iterative method is proposed to solve the M-matrix Sylvester equation, and the convergence analysis of the new method is given. Numerical experiments show that the new method is feasible and is effective under certain conditions.

关 键 词：SYLVESTER方程 M-矩阵 不动点迭代法 交替方向迭代法 

分 类 号：O241.6[理学—计算数学]