An iterative algorithm for approximating the sign function of tensors with the Einstein product

Abstract

We propose an iterative algorithm for computing the tensor sign function, a multidimensional generalization of the matrix sign function in case of higher dimensional data analysis. By considering traditional iterative techniques such as Newton’s method and Kovaric’s approach, we have developed an algorithm specifically designed for computing tensor sign function using the Einstein product. The method involved in our proposed algorithm exhibits fourth rate of convergence and ensures asymptotic stability. Through an extensive series of numerical experiments, we demonstrate the power and superiority of our algorithm compared to existing approaches. The outcomes depict the applicability of tensor computations, providing a highly efficient and accurate tool for addressing complex tensor problems. This work provides developments for tensor based algorithms, opening up new prospects in numerical analysis with potential applications across various disciplines in science and engineering.