正则 M­-矩阵代数 Riccati 方程最小非负解的一个注记

数学理论与应用 ›› 2021, Vol. 41 ›› Issue (4): 77-.

正则 M-矩阵代数 Riccati 方程最小非负解的一个注记

关晋瑞, 任孚鲛

太原师范学院数学系, 晋中, 030619

出版日期:2021-12-30 发布日期:2021-12-24

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

Guan Jinrui, Ren Fujiao

Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China

Online:2021-12-30 Published:2021-12-24
Contact: Guan Jinrui(1985), Linfen, Shanxi, Associate Professor, PhD, majoring in numerical linear algebra and its applications; Email: guanjinrui2012@163.com
Supported by:
This work is supported by the National Natural Science Foundation of China (Grant No. 12001395) and the Natural Science Foundation

of Shanxi province (Grant No. 201901D211423)

摘要/Abstract

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.

Abstract:

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.

Key words:

Algebraic, Riccati equation, Regular M--matrix; , Minimal nonnegative solution

关晋瑞, 任孚鲛.

正则 M-矩阵代数 Riccati 方程最小非负解的一个注记

[J]. 数学理论与应用, 2021, 41(4): 77-.

Guan Jinrui, Ren Fujiao.

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

[J]. Mathematical Theory and Applications, 2021, 41(4): 77-.