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
收藏
页码：992 / 1013
页数：22
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