## Abstract and Applied Analysis

### On the Iterative Method for the System of Nonlinear Matrix Equations

Asmaa M. Al-Dubiban

#### Abstract

The positive definite solutions for the system of nonlinear matrix equations $X+{A}^{\ast }{Y}^{-n}A=I,\mathrm{ Y}+{B}^{\ast }{X}^{-m}B=I$ are considered, where $n, m$ are two positive integers and A, B are nonsingular complex matrices. Some sufficient conditions for the existence of positive definite solutions for the system are derived. Under some conditions, an iterative algorithm for computing the positive definite solutions for the system is proposed. Also, the estimation of the error is obtained. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 685753, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511794

Digital Object Identifier
doi:10.1155/2013/685753

Mathematical Reviews number (MathSciNet)
MR3035381

Zentralblatt MATH identifier
1275.65022

#### Citation

Al-Dubiban, Asmaa M. On the Iterative Method for the System of Nonlinear Matrix Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 685753, 7 pages. doi:10.1155/2013/685753. https://projecteuclid.org/euclid.aaa/1393511794

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