RACSAM https://doi.org/10.1007/s13398-019-00696-3 ORIGINAL PAPER Further efficient hyperpower iterative methods for the computation of generalized inverses A (2) T ,S Predrag S. Stanimirovi´ c 1 · Ashim Kumar 2,3 · Vasilios N. Katsikis 4 Received: 1 September 2018 / Accepted: 27 May 2019 © The Royal Academy of Sciences, Madrid 2019 Abstract In this paper, we shall investigate new efficient variants of the hyperpower iterative methods for computing the generalized inverses A (2) T , S . Our main intention is to find efficient trans- formations of the hyperpower iterative method in order to minimize the number of required matrix by matrix products per cycle. In particular, we will transform the normalized hyper- power method of order 11 and the non-normalized hyperpower method of order 13 such that each of them requires six matrix by matrix products per iterative step. This will make the proposed methods quite computationally economic in comparison to the existing Schulz- type iterative methods. A variety of numerical experiments are also executed to manifest the capability and the practical applicability of our proposed iterative schemes. Additionally, it is also shown that the scalar by matrix multiplications involved in a non-normalized iterative method can reduce its computational efficiency in finding generalized inverses. Keywords Generalized outer inverse · Moore–Penrose inverse · Hyperpower method · Order of convergence · Computational complexity Mathematics Subject Classification 15A09 · 65F30 B Ashim Kumar ashimsingla1729@gmail.com Predrag S. Stanimirovi´ c pecko@pmf.ni.ac.rs Vasilios N. Katsikis vaskatsikis@econ.uoa.gr 1 Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia 2 Department of Mathematics, Panjab University Constituent College, Nihal Singh Wala, 142046, India 3 Department of Mathematical Sciences, I. K. Gujral Punjab Technical University Jalandhar, Kapurthala 144603, India 4 Division of Mathematics and Informatics, Department of Economics, National and Kapodistrian University of Athens, Athens, Greece 123