A fast and efficient Newton-Shultz-type iterative method for computing inverse and Moore-Penrose inverse of tensors

A fast and efficient newton-shultz-type iterative method is presented to computethe inverse of an invertible tensor. analysis of the convergence error shows that the proposedmethod has the sixth order convergence. it is shown that the proposed algorithm can be usedfor finding the moore-penrose inverse of tensors. computational complexities of the algorithmis presented to support the theoretical aspects of the paper. using the new method, we obtaina new preconditioner to solve the multilinear system a ∗n x = b. the effectiveness and accuracy of this method are re-verified by several numerical examples. finally, some conclusions aregiven.