The Positive Definite Solution of the Nonlinear Matrix Equation Xs−A*X−tA=Q. (12th March 2018) - Meng, Jie; Kim, Hyun-Min
ABSTRACT: In this paper, we consider a nonlinear matrix equation . The uniqueness of positive definite solution without any extra condition when s ≥ t is obtained. A fixed-point iteration with stepsize parameter for finding the positive definite solution is proposed. A condition number and some new perturbation bounds of the unique positive definite solution are derived. Finally, some numerical examples are given to show the eﬃciency of the proposed iterative method and perturbation bounds.