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中文摘要：
考虑非线性矩阵方程X＋A^＊X^-nA=P，其中A是m阶非奇异复矩阵，P是m阶Hermite正定矩阵，本文利用不动点理论讨论了该方程Hermite正定解的存在性及包含区间，给出了极大解的性质及求极大，极小解的迭代算法，研究了极大解的扰动问题，利用微分等方法获得了两个新的一阶扰动界，并给出数值例子对所得结果进行了比较说明。
英文摘要：
The nonlinear matrix equation X＋A^＊X^-nA=P is studied, where A is an m x m nonsingular matrix and P is an m x rn Hermite positive definite matrix. The existence of the Hermite positive definite solutions is studied and the properties of the maximal solution are discussed. Moreover, iteration algorithms for the maximal and the minimum solutions are offered. And by means of differential, two new first order perturbation bounds for the maximal solution are obtained. The results are illustrated by several numerical examples.
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