Iterative processes with arbitrary order of convergence for approximating generalized inverses

Abstract

A family of iterative schemes for finding approximate inverses of nonsingular matrices is suggested and established analytically. This class of methods can be used for finding the Moore-Penrose inverse of a rectangular complex matrix. The order of convergence is stated in each case, depending on the first non-zero parameter. For different examples, the accessibility of some schemes, that is, the set of initial estimations leading to convergence, is analyzed in order to select those with wider sets. This wideness is related with the value of the first non-zero value of the parameters defining the method. Finally, some numerical examples are provided to confirm the theoretical results and to show the feasibility and effectiveness of the new methods.