Notes on the Hermitian Positive Definite Solutions of a Matrix Equation

[摘要] 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.

[学科分类] 应用数学