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Note on the iterative methods for computing the generalized inverse over Banach spaces

In this paper, we construct iterative methods for computing the generalized inverse A  (2)T, S over Banach spaces, and also for computing the generalized Drazin inverses ad of Banach algebra element a. Moreover, we estimate the error bounds of the iterative methods for approximating A  (2)T, S or ad. Copyright © 2011 John Wiley & Sons, Ltd.