Positive Definite Solutions of the Matrix EquationXr-∑i=1mAi∗X-δiAi=I-Reference-Cited by-同舟云学术

Positive Definite Solutions of the Matrix EquationXr-∑i=1mAi∗X-δiAi=I

Published:2015 Issue: Volume:2015 Page:1-8
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Al-Dubiban Asmaa M.¹

Affiliation:

1. Faculty of Science and Arts, Qassim University, P.O. Box 1162, Buraydah 51431, Saudi Arabia

Abstract

We investigate the nonlinear matrix equationXr-∑i=1mAi∗X-δiAi=I, whereris a positive integer andδi∈(0,1], for i=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation. A sufficient condition for the equation to have a unique positive definite solution is established. An iterative algorithm is provided to compute the positive definite solutions for the equation and error estimate. Finally, some numerical examples are given to show the effectiveness and convergence of this algorithm.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2015/473965.pdf

Reference24 articles.

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3. Interpolation Theory and Its Applications

4. Remarks on the Control of Discrete-Time Distributed Parameter Systems

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