The Hermitian Positive Definite Solution of Matrix Equations and Its Application

In image processing, we must solve a system of linear equations Mx = f . By, we know the solving of the System Mx = f can be transformed to the solving of the equations X + A* X^-q A = I. In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X^-q A = I . We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively, and the property of numerical range of A , construct an iterative method for obtaining positive definite solutions of the equation at last.