In this paper, we construct a parametric family of iterative methods to compute the inverse of a nonsingular matrix. This class is free of inverse operators. We prove the third-order of convergence under some conditions involving the parameter of the family. Moreover, a dynamical analysis is made for the first time to a matrix iterative method, finding intervals of stability, that include but are wider than those found in the convergence analysis. Numerical tests on large random matrices confirm the results found.

中文翻译：

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权函数迭代法的逆矩阵估计及其稳定性分析


在本文中，我们构建了一系列参数迭代方法来计算非奇异矩阵的逆。此类没有逆运算符。我们证明了在涉及族参数的某些条件下的三阶收敛性。此外，首次对矩阵迭代方法进行了动力学分析，找到了稳定区间，该区间包括但比收敛分析中发现的区间更宽。对大型随机矩阵的数值测试证实了所发现的结果。