Iterative methods for computing generalized inverses

In this article we extend the method of Yong-Lin Chen [Yong-Lin Chen, Iterative methods for computing the generalized inverses AT,S(2) of a matrix A, Appl. Math. Comput. 75 (2–3) (1996) 207–222] to infinite dimensional settings. Precisely, we construct an iterative method for computing outer generalized inverses of operators on Banach spaces, and also for computing the generalized Drazin inverse of Banach algebra elements.