On the matrix equation X+AT 2m√X-1 A = I

被引：17

作者：

Ramadan, MA ^{[1
]}

El-Shazly, NM ^{[1
]}

机构：

[1] Menoufia Univ, Dept Math, Fac Sci, Shibin Al Kawm, Egypt

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 173卷 / 02期

关键词：

nonlinear matrix equation; positive definite matrix; extremal positive solutions iteration; necessary and sufficient conditions; matrix factorization;

D O I：

10.1016/j.amc.2005.04.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study iterative methods for finding the extremal positive definite solutions of the matrix equation X + (M)root X-1 A = I. First, a condition on the existence of a positive definite solution of this matrix equation is given. Then, the existence as well as the rate of convergence of some proposed algorithms to obtain the extremal positive definite solutions of this equation is presented. Moreover, a generalization of computationally simple and efficient known algorithm is applied for obtaining the extremal positive definite solutions. In addition, both the necessary and sufficient conditions for this matrix equation to have positive definite solution are presented. Numerical examples are given to illustrate the performance and the effectiveness of the algorithms. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：992 / 1013

页数：22

共 50 条

[41] Fixed-point accelerated iterative method to solve nonlinear matrix equation X - Σi=1mAi*X-1Ai = Q
Li, Tong
Peng, Jingjing
Peng, Zhenyun
Tang, Zengao
Zhang, Yongshen
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (08)
[42] Positive definite solution of the matrix equation X = Q - AX(-1)A
Berzig, Maher
Duan, Xuefeng
Samet, Bessem
[J]. MATHEMATICAL SCIENCES, 2012, 6 (01)
[43] PERTURBATION BOUNDS FOR THE MATRIX EQUATION X plus A*(X)over-cap -1A = Q
Hasanov, Vejdi, I
[J]. APPLIED AND COMPUTATIONAL MATHEMATICS, 2020, 19 (01) : 20 - 33
[44] Perturbation estimates for the nonlinear matrix equation X-A * X q A=Q (0<q<1)
Jia G.
Gao D.
[J]. Journal of Applied Mathematics and Computing, 2011, 35 (1-2) : 295 - 304
[45] On the matrix equation X = Q plus A*(Im ⊗ X - C)rA
Yao, Guozhu
Liao, Anping
Duan, Xuefeng
[J]. PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 3, 2009, : 106 - 110
[46] Solving the nonlinear matrix equation X = Q + Σi=1mMiXδiMi* via a contraction principle
Lim, Yongdo
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (04) : 1380 - 1383
[47] The iterative methods for solving nonlinear matrix equation X plus A☆X-1A plus B☆X-1B = Q
Vaezzadeh, Sarah
Vaezpour, Seyyed Mansour
Saadati, Reza
Park, Choonkil
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2013,
[48] On Hermitian positive definite solution of nonlinear matrix equation X plus A* X-2 A = Q
Guo, XX
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2005, 23 (05) : 513 - 526
[49] On Hermitian positive definite solutions of the nonlinear matrix equation X-A∗eXA = I
Gao D.
[J]. Journal of Applied Mathematics and Computing, 2016, 50 (1-2) : 109 - 116
[50] Perturbation analysis of the matrix equation X = Q+AH((X)over-cap-C)-1 A
Sun, JG
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 372 : 33 - 51

← 1 2 3 4 5 →