Approximating the Inverse and Moore-Penrose Inverse of Complex Matrices

Abstract

In this study, our prime objective is to compute the Moore-Penrose inverse (pseudo-inverse) of matrices that have complex entries. For this purpose, we propose an efficient algorithm that is iterative in working. In addition, we introduce the parametric fifth-order iterative scheme which is an extension of the previously established fourth-order iterative scheme. The proposed iterative scheme exhibits six-order convergence at specific values of the parameters. We also discuss the number of matrix multiplications per iteration and the CPU time as a comparison with the existing schemes.