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$leq$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.
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