HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X+A^{*}X^{-q}A=Q(q\geq 1)
矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

The Hermitian positive definite solutions of the matrix equaution $X+A^{*}X^{-q}A=Q(q\geq 1)$ is investigated. Some sufficient conditions and necessary conditions for the existence of positive definite solutions are given. An iterative method for computing Hermitian positive definite solutions is proposed. Numerical examples are given to illustrate the performance and the effectiveness of the iterative method.