M-矩阵代数Riccati方程的一类改进的交替线性化隐式迭代法（英文）  

A MODIFIED ALTERNATELY LINEARIZED IMPLICIT ITERATION METHOD FOR M-MATRIX ALGEBRAIC RICCATI EQUATION

作　　者：关晋瑞[1] 周芳[1] ZUBAIR Ahmed GUAN Jin-rui;ZHOU Fang;ZUBAIR Ahmed(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China;Institute of Mathematics and Computer Science,University of Sindh,Jamshoro,Pakistan)

机构地区：[1]太原师范学院数学系,山西晋中030619 [2]Institute of Mathematics and Computer Science,University of Sindh,Jamshoro,Pakistan

出　　处：《数学杂志》2019年第6期811-822,共12页Journal of Mathematics

基　　金：Supported in part by National Natural Science Foundation of China(11401424);Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2019L0783);Cultivate Scientific Research Excellence Programs of Higher Education Institutions in Shanxi(2019KJ035)

摘　　要：本文研究了M-矩阵代数Riccati方程的求解问题.基于交替线性化隐式迭代法,提出了一类改进的交替线性化隐式迭代法用于计算M-矩阵代数Riccati方程的最小非负解.在一定条件下证明了新方法的收敛性并给出最优参数表达式.数值实验表明,改进的方法在一定条件下是可行的.In this paper, we study the numerical solution of M-matrix algebraic Riccati equation. Based on the alternately linearized implicit iteration method, we propose a modified alternately linearized implicit iteration method(MALI) for computing the minimal nonnegative solution of MARE. Convergence of the MALI iteration method is proved under suitable conditions.Convergence rate with optimal parameters are given for the MARE associated with a nonsingular M-matrix or an irreducible singular M-matrix. Numerical experiments are given to show that the MALI iteration method is feasible in some cases.

关 键 词：代数RICCATI方程 最小非负解 M-矩阵 ALI迭代法 

分 类 号：O241.6[理学—计算数学]