On Hermitian Positive Definite Solutions of Matrix Equation $X-A^*X^{-2}A=I$

Abstract

The Hermitian positive definite solutions of the matrix equation $X-A^*X^{-2}A=I$ are studied. A theorem for existence of solutions is given for every complex matrix $A$. A solution in case $A$ is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.