非线性矩阵方程X+A~* X^(-q) A=Q的Hermite正定解

The Hermite Positive Definite Solution of the Nonlinear Matrix Equation X+A~* X(-q) A=Q

非线性矩阵方程X+A*X-qA=Q,这里A是n阶非奇异复数阵,Q为q≥1阶Hermite正定距阵.在q≥1时上面矩阵方程有正定解,或者是此正定解唯一,并给出它们的充分以及必要条件,接着又给出了求上面方程正定解的迭代法.

Nonlinear Q is of n order Hermite, positive definite solution, and necessary conditions matrix equation X ＋A ＊ X-qA = Q, here A is the order nonsingular complex matrix, and it is positive definite matrix. When q≥ 1, the above matrix equation has a or it is the only one positive definite solution, at the same time, their sufficient are given, and then definite the above equations iterative method.