On hyperpower family of iterations for computing outer inverses possessing high efficiencies

Hyperpower iteration is a powerful family of iterative methods for finding outer inverses with arbitrary order of convergence p≥2p≥2. In this paper, we present several systematic algorithms for factorizations of the hyperpower iterative family of arbitrary orders with a view to reduce the necessary number of multiplications in each iterative step. Additionally, effective heuristics for factoring arbitrary higher orders hyperpower iteration are presented. The new formulations of the hyperpower iterative steps are convergent with higher computational efficiency indices.