一类广义Stein方程的正定解

Positive Definite Solution for a Class of Generalized Stein Equation

基于Thompson度量的良好性质,给出一类广义Stein方程存在正定解的充分条件;构造求解的迭代方法,并给出该迭代方法的误差估计式;最后用数值例子验证了该迭代方法的可行性。

Based on the elegant properties of the Thompson metric,we give a sufficient condition for the existence of positive definite solution for a class of generalized Stein equation.An iterative method is proposed to compute the positive definite solution,and its error estimate formula is also derived.Numerical examples show that this iterative method is feasible.