A Recursive Algorithm for Computing the Weighted Moore-Penrose Inverse $A^+_{MN}$

Abstract

In this paper, we give a recursive algorithm for computing the weighted Moore-Penrose inverse $A^+_{MN}$. This method is a generalization of Greville's method for computing Moore-Penrose inverse $A^+$, and the technique of its proof is new. This method suits the weighted least-squares problem.