A Family of higher-order convergent iterative methods for computing the Moore–Penrose inverse

Abstract

In this paper, we extend the iterative method for computing the inner inverse of a matrix proposed in Li and Li [W.G. Li, Z. Li, A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix, Applied Mathematics and Computation 215 (2010) 3433–3442] to compute the Moore–Penrose inverse of a matrix, and show that the generated sequence converges to the Moore–Penrose inverse of a matrix in a higher order. The performance of the method is tested on some randomly generated matrices.