矩阵方程X-A~*X^qA=Q(q>0)的Hermite正定解

HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X - A~*X^qA=Q(q>0)

本文讨论了矩阵方程X-A*XqA=Q(q>0)的Hermite正定解,给出了q>1时解存在的必要条件,存在区间,以及迭代求解的方法．证明了0<q<1时解的存在唯一性．

We study the Hermitian positive definite solutions of the matrix equation X - A＊XqA = Q with q 〉 0. When q 〉 1, a necessary condition for existence is given and the basic fixed point iterations for the equation are discussed in some detail. When 0 〈 q 〈 1, it shows that there exists a uique positive definite solution to the equation.