A further study on a nonlinear matrix equation

被引：2
|
作者：
Meng, Jie [1 ]
Chen, Hongjia [2 ]
Kim, Young-Jin [1 ]
Kim, Hyun-Min [1 ,3 ]
机构：
[1] Pusan Natl Univ, Finance Fishery Manufacture Ind Math Ctr Big Data, Busan 46241, South Korea
[2] Nanchang Univ, Sch Sci, Dept Math, Nanchang 30031, Jiangxi, Peoples R China
[3] Pusan Natl Univ, Dept Math, Busan 46241, South Korea
来源：
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2020年 / 37卷 / 03期
基金：
中国国家自然科学基金; 新加坡国家研究基金会;
关键词：
Matrix equation; Symmetric positive definite; Cyclic reduction; Structured condition number; POSITIVE-DEFINITE SOLUTION; BOUNDS; STABILITY; SYSTEMS;
D O I：
10.1007/s13160-020-00421-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The nonlinear matrix equation Xp = R + MT (X -1 + B)-1 M, where p is a positive integer, M is an arbitrary n x n real matrix, R and B are symmetric positive semidefinite matrices, is considered. When p = 1, this matrix equation is the well-known discrete-time algebraic Riccati equation (DARE), we study the convergence rate of an iterative method which was proposed in Meng and Kim (J Comput Appl Math 322:139-147, 2017). For the generalized case p = 1, a structured condition number based on the classic definition of condition number is defined and its explicit expression is obtained. Finally, we give some numerical examples to show the sharpness of the structured condition number.
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页码：831 / 849
页数：19
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