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