Abstract This paper provides a novel inversion free variant of the fixed point iteration strategy to obtain a maximal positive definite solution for the nonlinear matrix equation X + A ⁎ X − 1 A = Q . The conditions for the convergence of the method and for the existence of solution of this nonlinear matrix equation are derived. At the end, numerical examples are also presented to show the behavior of the proposed technique.

中文翻译：

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求解非线性矩阵方程的一种新的迭代方法

摘要 本文提供了一种新的不动点迭代策略的无反演变体，以获得非线性矩阵方程 X + A ⁎ X − 1 A = Q 的最大正定解。推导出了该方法收敛的条件和该非线性矩阵方程解存在的条件。最后，还提供了数值例子来展示所提出技术的行为。