Work

Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

Year: 2014

Type: article

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

Source: Journal of Applied Mathematics

DOI: 10.1155/2014/128249

Authors: Jing Li, Yuhai Zhang

Institution: Shandong University

Language: Latvian

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,130

Funders: Shandong University, National Natural Science Foundation of China, Natural Science Foundation of Shandong Province, Independent Innovation Foundation of Shandong University