正则M-矩阵代数Riccati方程最小非负解的一个注记  

A Note on the Minimal Nonnegative Solution for Regular M-matrix Algebraic Riccati Equations

作　　者：关晋瑞[1] 任孚鲛[1] Guan Jinrui;Ren Fujiao(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,晋中030619

出　　处：《数学理论与应用》2021年第4期77-82,共6页Mathematical Theory and Applications

基　　金：This work is supported by the National Natural Science Foundation of China(Grant No.12001395);the Natural Science Foundation of Shanxi province(Grant No.201901D211423)。

摘　　要：关于M-矩阵代数Riccati方程的理论与有效数值方法的研究是近年来的一个热点问题本文研究M-矩阵代数Riccati方程最小非负解的存在性,给出当系数矩阵为正则M-矩阵时方程存在最小非负解的一个新证明,这比原有证明要简单得多.此外,我们给出一个更广泛的条件来保证方程最小非负解的存在性,这是现有结果的一个扩展.Research on the theories and efficient numerical methods of M-matrix algebraic Riccati equations(MARE)has become a hot topic in recent years.In this paper,we study the existence of minimal nonnegative solution for MARE and give a new proof to the existence of minimal nonnegative solution for the MARE associated with a regular M-matrix,which is much simpler than the original proof In addition,we give a wider condition to guarantee the existence of minimal nonnegative solution for the MARE,which is an extension of the existing results.

关 键 词：代数RICCATI方程 正则M-矩阵 最小非负解 

分 类 号：O241.6[理学—计算数学]