An iterative method to compute Moore-Penrose inverse based on gradient maximal convergence rate

Abstract

In this paper, we present an iterative method based on gradient maximal convergence rate to compute Moore-Penrose inverse A† of a given matrix A. By this iterative method, when taken the initial matrix X0 = A*, the M-P inverse A† can be obtained with maximal convergence rate in absence of roundoff errors. In the end, a numerical example is given to illustrate the effectiveness, accuracy and its computation time, which are all superior than the other methods for the large singular matrix.