Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme

Abstract

The goal of this research is to extend and investigate an improved approach for calculating the weighted Moore-Penrose (WMP) inverses of singular or rectangular matrices. The scheme is constructed based on a hyperpower method of order ten. It is shown that the improved scheme converges with this rate using only six matrix products per cycle. Several tests are conducted to reveal the applicability and efficiency of the discussed method, in contrast with its well-known competitors.