Positive definite solutions of the matrix equations X +/- A*X(-q)A = Q (q >= 1)
In this paper we investigate nonlinear matrix equations X +/- A*X(-q)A = Q where q >= 1. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X +/- A*X(-q)A = Q to have two different positive definite solutions and several sufficient conditions for the equation X +/- A*X(-q)A = Q to have a unique positive definite solution. We also propose iterative methods for obtaining positive definite solutions of these equations. Numerical examples are given to illustrate the effectiveness of the methods. (C) 2010 Elsevier Ltd. All rights reserved.
positive definite solution nonlinear matrix equation iterative method fixed point theorem