On thematrix equation X + AX-1A-BX-1B = I

被引：4

作者：

Hasanov, Vejdi Ismailov ^{[1
]}

机构：

[1] Konstantin Preslavsky Univ Shumen, Fac Math & Informat, Shumen, Bulgaria

来源：

LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 09期

关键词：

Nonlinear matrix equation; positive definite solution; iterative method; POSITIVE-DEFINITE SOLUTION; SUFFICIENT CONDITIONS; EXTREME SOLUTIONS; MATRIX; EXISTENCE;

D O I：

10.1080/03081087.2017.1373730

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the matrix equation X + A * X -1A B * X -1B = I. Some sufficient and necessary conditions for the existence of Hermitian positive definite solutions as well as for the existence of the smallest Hermitian positive definite solution of the considered equation are derived. Two iterative methods for computing the smallest positive definite solution are proposed. Some numerical examples are presented to illustrate the theoretical results.

引用

页码：1783 / 1798

页数：16

共 24 条

[1] On some sufficient conditions for the existence of a positive definite solution of the matrix equation X plus A*X-1A - B*X-1B = I
Ali, Aynur A.
Hasanov, Vejdi I.
[J]. 41ST INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'15), 2015, 1690
[2] POSITIVE SOLUTIONS TO X = A-BX-1B-STAR
ANDERSON, WN
MORLEY, TD
TRAPP, GE
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 134 : 53 - 62
[3] ALGORITHM - SOLUTION OF MATRIX EQUATION AX+XB = C
BARTELS, RH
STEWART, GW
[J]. COMMUNICATIONS OF THE ACM, 1972, 15 (09) : 820 - &
[4] Berzig M, 2012, MATH SCI, V6, DOI 10.1186/2251-7456-6-27
[5] Deimling K., 1985, Nonlinear functional analysis, DOI DOI 10.1007/978-3-662-00547-7
[6] Positive definite solution of a class of nonlinear matrix equation
Duan, Xue-Feng
Wang, Qing-Wen
Li, Chun-Mei
[J]. LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (06) : 839 - 852
[7] NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF A POSITIVE-DEFINITE SOLUTION OF THE MATRIX EQUATION X+A-ASTERISK-X-1A=Q
ENGWERDA, JC
RAN, ACM
RIJKEBOER, AL
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 186 : 255 - 275
[8] ON THE EXISTENCE OF A POSITIVE-DEFINITE SOLUTION OF THE MATRIX EQUATION X=A(T)X(-1)A=I
ENGWERDA, JC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 194 : 91 - 108
[9] Hermitian solutions of the equation X=Q+NX(-1)N*
Ferrante, A
Levy, BC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 247 : 359 - 373
[10] Golub G. H., 2013, Matrix Computations

← 1 2 3 →

On thematrix equation X + A*X-1A-B*X-1B = I

On thematrix equation X + AX-1A-BX-1B = I