Computing tensor sign function using a sixth-order iterative method based on the Einstein product

Purpose The purpose of this paper is to propose a novel sixth-order iterative method for the computation of the sign function of tensors, which is the generalization of the matrix sign function. Design/methodology/approach The method is generated using the Einstein product of tensors and implementing the product to the corresponding tensor equation associated with the sign function. Findings Convergence analysis of the proposed method has been investigated by proving that the sequence attained from the proposed scheme converges to the sign of the given tensor with a sixth-order convergence. Asymptotic stability of the method has also been presented by considering the numerical perturbation obtained at each iterate. Originality/value Various numerical experiments have been presented to justify the superiority of the method in terms of accuracy and number of iterations. For this, we have considered tensors of different orders and dimensions.