GIBS: a general and efficient iterative method for computing the approximate inverse and Moore–Penrose inverse of sparse matrices based on the Schultz iterative method with applications

Abstract

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.