The Hermitian Positive Definite Solution of Matrix Equations X+A.X-1A = I

被引：0
作者：
Wei, Peiyu [1 ]
Tan, Boxue [1 ]
Liu, Xueting [1 ]
机构：
[1] Shandong Univ Technol, Sch Elect & Elect Engn, Zibo 255049, Shandong, Peoples R China
来源：
2009 2ND IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY, VOL 4 | 2009年
关键词：
matrix equation; Hermitian positive definite solutions; iterative method; image processing; EXISTENCE; ITERATION;
D O I：
10.1109/ICCSIT.2009.5234511
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we discuss the Hermitian positive definite solutions of the nonlinear matrix equation X+A(.)X(-1)A = I. we give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of equation(1.1). Based on them, we also present some properties of the coefficient matrix A are presented and two equivalent equation of equation(1.1) when the matrix equation has a Hermitian positive definite solution. And construct an iterative methods for obtaining the Hermitian positive definite solutions of the equation are constructed.
引用
收藏
页码：497 / +
页数：2
相关论文
共 16 条
[1]   DIRECT METHODS FOR SOLVING POISSONS EQUATIONS [J].
BUZBEE, BL ;
GOLUB, GH ;
NIELSON, CW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1970, 7 (04) :627-&
[2]   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
[3]   A new inversion free iteration for solving the equation X+A*X-1 A=Q [J].
El-Sayed, SM ;
Al-Dbiban, AM .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 181 (01) :148-156
[4]   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
[5]  
ELSAYED SM, 2001, SIAM J MATRIX ANAL A, V23, P632
[6]   Hermitian solutions of the equation X=Q+NX(-1)N* [J].
Ferrante, A ;
Levy, BC .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 247 :359-373
[7]   A note on the fixed-point iteration for the matrix equations X ± A*X-1 A = I [J].
Fital, Sandra ;
Guo, Chun-Hua .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (8-9) :2098-2112
[8]   On two perturbation estimates of the extreme solutions to the equations X ± A*X-1A = Q [J].
Hasanov, VI ;
Ivanov, IG .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 413 (01) :81-92
[9]  
[heng Mingsong 程明松], 2005, [北京大学学报. 自然科学版, Acta Scientiarum Naturalium Universitatis Pekinensis], V41, P55
[10]  
Horn R. A., 2013, Matrix analysis, Vsecond
12