A new inversion free iteration for solving the equation X+A*X-1 A=Q

被引：51

作者：

El-Sayed, SM ^{[1
]}

Al-Dbiban, AM

机构：

[1] Educ Coll Girls, Dept Math, Buraydah, Al Qassim, Saudi Arabia

[2] Benha Univ, Fac Sci, Dept Math, Benha 13518, Saudi Arabia

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2005年 / 181卷 / 01期

关键词：

matrix equation; inversion free variant of the basic fixed point iteration methods; convergence rate;

D O I：

10.1016/j.cam.2004.11.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new inversion free variant of the basic fixed point iteration method for obtaining a maximal positive definite solution of the nonlinear matrix equation X + A*X-1 A = Q. It is more accurate than Zhan's algorithm (J. Sci. Comput. 17 (1996) 1167) and has less number of operations than the algorithm of Guo and Lancaster (Math. Comput. 68 (1999) 1589). We derive convergence conditions of the iteration and existence conditions of a solution to the problem. Finally, we give some numerical results to illustrate the behavior of the considered algorithm. (c) 2004 Elsevier B.V. All rights reserved.

引用

页码：148 / 156

页数：9

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