Two iteration processes for computing positive definite solutions of the equation X-A*X-nA = Q

Authors
El-Sayed, SM
Citation
Sm. El-sayed, Two iteration processes for computing positive definite solutions of the equation X-A*X-nA = Q, COMPUT MATH, 41(5-6), 2001, pp. 579-588
Citations number
10
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN journal
08981221 → ACNP
Volume
41
Issue
5-6
Year of publication
2001
Pages
579 - 588
Database
ISI
SICI code
0898-1221(200103)41:5-6<579:TIPFCP>2.0.ZU;2-J
Abstract
In the present paper, we suggest two iteration methods for obtaining positi ve definite solutions of nonlinear matrix equation X-A*X(-n)A = Q, for the integer n greater than or equal to 1. We obtain sufficient conditions for e xistence of the solutions for the matrix equation. Finally some numerical e xamples to illustrate the effectiveness of the algorithms and some remarks. (C) 2001 Elsevier Science Ltd. All rights reserved.