In this paper, an algorithm is proposed to compute the inverse of an invertible matrix. The new algorithm is a generalization of the algorithms based on the well-known Schultz-type iterative methods. We show that the convergence order of the new method is a linear combination of the Fibonacci sequence and also is powerful and efficient in finding and keeping sparsity of the obtained approximate inverse of sparse matrices. The convergence of the algorithm is analysed and some applications are studied. It is shown that the proposed algorithm can be used for computing an approximation of the Moore–Penrose inverse of matrices. Numerical examples are provided to verify the feasibility and effectiveness of the new method.

在本文中，提出了一种计算可逆矩阵的逆的算法。新算法是基于著名的舒尔茨型迭代方法的算法的推广。我们证明了新方法的收敛阶是斐波那契序列的线性组合，并且在寻找和保持所获得的稀疏矩阵的近似逆的稀疏性方面也是强大而有效的。分析了算法的收敛性并研究了一些应用。结果表明，所提出的算法可用于计算摩尔-彭罗斯逆矩阵的近似值。算例验证了新方法的可行性和有效性。