On Hermitian Positive Definite Solutions of a Type of Nonlinear Matrix Equations and Application
Hongkui Li, Xueting Liu · 2009
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X+A*X-2A=I are studied. We present some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on the necessary and sufficient conditions, some properties when the matrix equation has a Hermitian positive definite solution, and an iterative method for finding the maximal solution are given.