Higher-Order Convergent Iterative Method for Computing the Generalized Inverse over Banach Spaces

Abstract

A higher-order convergent iterative method is provided for calculating the generalized inverse over Banach spaces. We also use this iterative method for computing the generalized Drazin inverse $a^d$ in Banach algebra. Moreover, we estimate the error bounds of the iterative methods for approximating $A_{T,S}^{\left(2\right)}$ or $a^d$.