SOLUTION AND PERTURBATION ESTIMATES FOR THE MATRIX EQUATION X-A*X-2A=Q
矩阵方程X-A*X-2A=Q的正定解及其扰动分析

Consider the nonlinear matrix equation X-A*X-2A=Q, where Q is Hermitian positive definite. It is proved that the matrix equation has a unique Hermitian ositive definite solution provided a:=2||A||22||Q-1||23<1, and under this condition, a perturbation bound for the Hermitian positive definite solution is derived. Moreover, an explicit expression of the condition number for the Hermitian positive definite solution is offered. The results are illustrated by some numerical examples.