A hyperpower iterative method for computing the generalized Drazin inverse of Banach algebra element

Abstract

A quadratically convergent Newton-type iterative scheme is proposed for approximating the generalized Drazin inverse b d of the Banach algebra element b. Further, its extension into the form of the hyperpower iterative method of arbitrary order p ! 2 is presented. Convergence criteria along with the estimation of error bounds in the computation of b d are discussed. Convergence results confirms the high order convergence rate of the proposed iterative scheme.