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.
"Notes on the Hermitian Positive Definite Solutions of a Matrix Equation." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/128249