On the Nonlinear Matrix Equation $X^s + A^*F(X)A = Q$ with $S≥ 1$

Abstract

This work is concerned with the nonlinear matrix equation $X^s + A^*F(X)A= Q$ with $s ≥ 1$. Several sufficient and necessary conditions for the existence and  uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.