The Hermitian positive definite solution and its perturbation problem of the nonlinear matrix equation X-A*(R+B*XB)-t A=Q(1＜t≤1)are studied.The sufficient conditions and necessary conditions for the existence of the solution of the matrix equation are given.By using matrix partial order and fixed point theorem,the inclusion interval and existence of the Hermite positive definite solution of the matrix equation are discussed,the value range is obtained and further accurate.An iterative method for calculating the unique Hermite positive definite solution of the matrix equation is constructed and the first order perturbation bound are derived.Finally,numerical examples are given to verify the effectiveness and feasibility of the proposed method.
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