M-矩阵代数Riccati方程的一类新的迭代解法  

A New Iteration Method for M-matrix Algebraic Riccati Equations

作　　者：关晋瑞[1] 任孚鲛[1] 邵荣侠 GUAN Jinrui;REN Fujiao;SHAO Rongxia(Depurtment of Mathematics,Taixuan Normal University,Jinzhong 030619,China;School of Statistics and Data Science,Xinjiang Unioersity of Finance and Economics,Urumqi 830012,China)

机构地区：[1]太原师范学院数学系,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：《应用数学》2021年第3期611-618,共8页Mathematica Applicata

基　　金：Supported in part by the National Natural Science Foundation of China(11401424);the Natural Science Foundation of Shanxi province(201901D211423);the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2019L0783)。

摘　　要：本文研究M-矩阵代数Riccati方程的数值解法.利用适当的变换将方程转化为其离散形式,进而提出了一种新的迭代法来计算方程的最小非负解.通过选取合适的迭代参数,证明了新方法的收敛性.理论分析和数值实验表明,新方法是可行的,而且在一定情况下比现有的几类方法更加有效.In this paper,we consider numerical solution of the M-matrix algebraic Riccati equation(MARE).We propose a new iteration method for computing the minimal nonnegative solution of the MARE,which is obtained by transforming the MARE to its discrete form.Convergence of the new iteration method is proved by choosing proper parameters for the MARE.Theoretical analysis and numerical experiments are given to show that the new iteration method is feasible and is effective than some existing methods under certain conditions.

关 键 词：代数RICCATI方程 M-矩阵 最小非负解 牛顿法 ALI迭代法 

分 类 号：O241.6[理学—计算数学]