Abstract
In this paper, we consider a nonlinear matrix equation. We propose necessary and sufficient conditions for the existence of Hermitian positive definite solutions. Some necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions of this equation is also derived. Based on the Banach fixed point theorem, the existence and the uniqueness of the Hermitian positive definite solution are studied. An iterative method for obtaining the Hermitian positive definite solution of this equation is proposed. Finally, some numerical examples are presented to illustrate the performance and efficiency of the proposed algorithm.
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