On positive definite solutions of the nonlinear matrix equation X+A★X−nA=I

摘要

In this paper, some properties of a positive definite solution of the nonlinear matrix equation X+A★X−nA=I are discussed. Effective iterative methods to obtain the smallest positive definite solution are established. Moreover, the necessary and sufficient conditions for existence the smallest positive definite solution are obtained. Finally, some numerical results are given.