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

• # Keywords

Generalized inverse; Drazin inverse; generalized Drazin inverse; Banach algebra; iterative method; convergence analysis.

• # Abstract

A quadratically convergent Newton-type iterative scheme is proposed for approximating the generalized Drazin inverse bd 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 bd are discussed. Convergence results confirms the high order convergence rate of the proposed iterative scheme.

• # Author Affiliations

1. Department of Mathematics, School of Arts & Sciences, Amrita Vishwa Vidyapeetham, Amrita University, Amritapuri, India
2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India
3. Faculty of Sciences and Mathematics, University of Nis., Visegradska 33, 18000 Nis, Serbia
4. Department of Mathematics, NIT Hamirpur, Hamirpur, India