求解非线性矩阵方程是数值代数领域研究的重要课题之一，它在控制理论，运输理论，动态规划，统计学和椭圆微分方程的差分方法求解等多个领域有着广泛的应用．本文根据不动点理论，通过构造单调迭代序列，讨论了非线性矩阵方程X＋A＊A^-1A＋B^＊X^-2=I艾米特正定解存在性条件及迭代求解方法．%Solving nonlinear matrix equations is one of important topics in the fields of numerical algebra. It is widely used in many areas, such as control theory, transport theory, dynamic programming, statistics, the finite difference method of Elliptic differential equations etc. In this paper, the existence condition and iteration method of hermite solution of nonlinear matrix equation are discussed, by constructing the monotone iterative sequence according to the fixed point theory.
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