Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

Jing Li and Yuhai Zhang

Journal of Applied Mathematics, 2014, vol. 2014, 1-8

Abstract:

The nonlinear matrix equation, with is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some properties of the unique Hermitian positive definite solution are obtained. A residual bound of an approximate solution to the equation is evaluated. The theoretical results are illustrated by numerical examples.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:128249

DOI: 10.1155/2014/128249

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