Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2014 English Publisher:WileyJournal:Journal of Applied Mathematics, volume 2,014, pages 1-8 (issn: 1110-757X, eissn: 1687-0042,

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Authors: Jing Li 0004; Yuhai Zhang;

doi: 10.1155/2014/128249

Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

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Abstract

The nonlinear matrix equation,X-∑i=1mAi*XδiAi=Q,with-1≤δi<0is 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.

Related Organizations

Shandong Women’s University
China (People's Republic of)

Keywords

Numerical methods for matrix equations, QA1-939, Matrix equations and identities, Mathematics

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