M-矩阵代数Riccati方程的一类简单迭代法  

A Simple Iteration Method for M-matrix Algebraic Riccati Equations

作　　者：关晋瑞 任孚鲛[1] 邵荣侠 GUAN Jin-rui;REN Fu-jiao;SHAO Rong-xia(School of Mathematics and Statistics,Taiyuan Normal University,J inzhong,Shanxi,030619,China;School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi,Xinjiang,830012,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619 [2]新疆财经大学统计与数据科学学院,新疆乌鲁木齐830012

出　　处：《新疆师范大学学报（自然科学版）》2023年第3期1-5,12,共6页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：国家自然科学基金项目(12001395);山西省科技创新人才团队专项资助项目(202204051002018)。

摘　　要：文章研究了M-矩阵代数Riccati方程的数值解法。当方程的系数矩阵为正则奇异M-矩阵时,现有的一些数值方法在计算中存在一定程度的困难。为此提出了一类简单迭代法以求解方程,该方法在每步迭代中只用到矩阵乘法,运算量小且易于实现。理论分析和数值实验表明该方法是可行的,而且在一定情况下有效。This paper studies numerical solution of M-matrix algebraic Riccati equations.When the coefficient matrix of the equation is a regular singular M-matrix,some existing numerical methods encounter certain difficulties.Therefore,a simple iteration method is proposed to solve the equation.This method only uses matrix multiplication in each iteration,with small computational complexity and easy implementation.Theoretical analysis and numerical experiments show that the method in this paper is feasible and effective under certain circumstances.

关 键 词：代数RICCATI方程 正则M-矩阵 牛顿法 迭代法 

分 类 号：O241.6[理学—计算数学]