On the Maximal Positive Definite Solution of the Nonlinear Matrix Equation X − ∑ mi = 1 A ∗i X − 1 A i + ∑ nj = 1 B ∗j X − 1 B j = I

Authors

Mohamed A. Ramadan, Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, EgyptFollow
Naglaa M. El – Shazly, Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, the existence and uniqueness of the maximal positive definite solution of the nonlinear matrix equation X − ∑mi=1 A∗i X −1 Ai + ∑nj=1 B∗j X −1 B j = I is studied. Our technique is based on the coupled fixed-point theorem. A sufficient condition for the existence of the unique maximal solution of the above nonlinear matrix equation is investigated. Some numerical examples are presented to show the applicability and the effectiveness of our technique.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140220

Recommended Citation

A. Ramadan, Mohamed and M. El – Shazly, Naglaa (2020) "On the Maximal Positive Definite Solution of the Nonlinear Matrix Equation X − ∑ mi = 1 A ∗i X − 1 A i + ∑ nj = 1 B ∗j X − 1 B j = I," Applied Mathematics & Information Sciences: Vol. 14: Iss. 2, Article 20.
DOI: http://dx.doi.org/10.18576/amis/140220
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss2/20