An efficient hyperpower iterative method for computing weighted MoorePenrose inverse

Abstract

In this paper, we propose a new hyperpower iterative method for approximating the weighted Moore-Penrose inverse of a given matrix. The main objective of the current work is to minimize the computational complexity of the hyperpower iterative method using some transformations. The proposed method attains the fifth-order of convergence using four matrix multiplications per iteration step. The theoretical convergence analysis of the method is discussed in detail. A wide range of numerical problems is considered from scientific literature, which demonstrates the applicability and superiority of the proposed method.