A fast convergent iterative solver for approximate inverse of matrices

SUMMARY In this paper, a rapid iterative algorithm is proposed to find robust approximations for the inverse of nonsingular matrices. The analysis of convergence reveals that this high-order method possesses eighth-order convergence. The interesting point is that, this rate is attained using less number of matrix-by-matrix multiplications in contrast to the existing methods of the same type in the literature. The extension of the method for finding Moore–Penrose inverse of singular or rectangular matrices is also presented. Numerical comparisons will be given to show the applicability, stability and consistency of the new scheme by paying special attention on the computational time. Copyright © 2013 John Wiley & Sons, Ltd.

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