A Rapid Numerical Algorithm to Compute Matrix Inversion

Abstract EN

The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses.

It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges.

Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.