Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation
Wei-Juan Pei, Guoxing Wu, Duanmei Zhou, Yitian Liu · International Journal of Computer Mathematics · 2013
In this paper, the Hermitian positive-definite solutions of the matrix equation Xs+A*X−tA=Q are considered. New necessary and sufficient conditions for the equation to have a Hermitian positive-definite solution are derived. In particular, when A is singular, a new estimate of Hermitian positive-definite solutions is obtained. In the end, based on the fixed point theorem, an iterative algorithm for obtaining the positive-definite solutions of the equation with Q=I is discussed. The error estimations are found.