Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation

被引：4
作者：
Pei, Weijuan [1 ]
Wu, Guoxing [1 ]
Zhou, Duanmei [2 ]
Liu, Yitian [1 ]
机构：
[1] Northeast Forestry Univ, Dept Math, Harbin 150040, Peoples R China
[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2014年 / 91卷 / 05期
关键词：
nonlinear matrix equation; Hermitian positive-definite solution; necessary and sufficient condition; iteration; SUFFICIENT CONDITIONS; EXISTENCE; X-S+A-ASTERISK-X(-T)A;
D O I：
10.1080/00207160.2013.819425
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the Hermitian positive-definite solutions of the matrix equation X-s + A*X(-t)A = Q are considered. New necessary and sufficient conditions for the equation to have a Hermitian positive-definite solution are derived. In particular, when A is singular, a new estimate of Hermitian positive-definite solutions is obtained. In the end, based on the fixed point theorem, an iterative algorithm for obtaining the positive-definite solutions of the equation with Q = I is discussed. The error estimations are found.
引用
收藏
页码：872 / 880
页数：9
相关论文
共 17 条
[1]   POSITIVE SOLUTIONS TO X = A-BX-1B-STAR [J].
ANDERSON, WN ;
MORLEY, TD ;
TRAPP, GE .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 134 :53-62
[2]  
Bhatia R., 2013, MATRIX ANAL
[3]   On the Hermitian positive definite solutions of nonlinear matrix equation Xs + A*X-tA = Q [J].
Cai, Jing ;
Chen, Guoliang .
APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (01) :117-123
[4]   Some investigation on Hermitian positive definite solutions of the matrix equation Xs + A*X-tA = Q [J].
Cai, Jing ;
Chen, Guoliang .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (8-9) :2448-2456
[5]   On the existence of Hermitian positive definite solutions of the matrix equation Xs+A*X-t A=Q [J].
Duan, Xuefeng ;
Liao, Anping .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (04) :673-687
[6]   Some properties for the existence of a positive definite solution of matrix equation X+A☆X-2m A = I [J].
El-Sayed, SM ;
El-Alem, M .
APPLIED MATHEMATICS AND COMPUTATION, 2002, 128 (01) :99-108
[7]   On an iteration method for solving a class of nonlinear matrix equations [J].
El-Sayed, SM ;
Ran, ACM .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2002, 23 (03) :632-645
[8]   NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF A POSITIVE-DEFINITE SOLUTION OF THE MATRIX EQUATION X+A-ASTERISK-X-1A=Q [J].
ENGWERDA, JC ;
RAN, ACM ;
RIJKEBOER, AL .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 186 :255-275
[9]   ON THE EXISTENCE OF A POSITIVE-DEFINITE SOLUTION OF THE MATRIX EQUATION X=A(T)X(-1)A=I [J].
ENGWERDA, JC .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 194 :91-108
[10]   Improved methods and starting values to solve the matrix equations X±A*X-1A=I iteratively [J].
Ivanov, IG ;
Hasanov, VI ;
Uhlig, F .
MATHEMATICS OF COMPUTATION, 2005, 74 (249) :263-278
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