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中文摘要：
提出了求非线性矩阵方程X＋A^TX^-1A＋B^TX^-1B=Q最大正定解的一个无逆迭代法.证明了由该算法产生的迭代序列单调递增有上界且收敛于原方程的最大正定解.数值实验表明该算法是十分有效的.
英文摘要：
This paper presents the maximal positive definite solution of the nonlinear matrix equation X ＋ A^TX^-1A ＋ B^TX^-1B = Q with an inversion-free iterative method,and proves that the sequences generated by the iterative schemes are monotonically increasing and weakening above. Numerical experiments further show the effectiveness of the new methods.
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