A New Family of Second-Order Iterative Methods for Computing the Moore Penrose Inverse Based on Penrose Equations

Abstract

A new family of second-order iterative algorithms for computing the Moore-Penrose inverse is developed. The construction of this algorithm is based on the usage of Penrose Equations ( 1) and (2). Convergence properties are considered. Numerical results are also presented and a comparison with Newton's method is made. It is observed that the new methods require less number of iterations than that of Newton's method. In addition, numerical experiments show that these methods are more effective than Newton's method when the number of columns increases than the number of rows.