Abstract and Applied Analysis

Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X = Q + A ( X ^ C ) 1 A

Dongjie Gao

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Abstract

We consider the nonlinear matrix equation X = Q + A ( X ^ C ) 1 A , where Q is positive definite, C is positive semidefinite, and X ^ is the block diagonal matrix defined by X ^ = d i a g ( X , X , , X ) . We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 216035, 4 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393447687

Digital Object Identifier
doi:10.1155/2013/216035

Mathematical Reviews number (MathSciNet)
MR3095349

Zentralblatt MATH identifier
1291.15038

Citation

Gao, Dongjie. Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation $X=Q+{A}^{\ast }{(\stackrel{^}{X}-C)}^{-1}A$. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 216035, 4 pages. doi:10.1155/2013/216035. https://projecteuclid.org/euclid.aaa/1393447687


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