Iterative refinement method by higher-order singular value decomposition for solving multi-linear systems

Abstract

In this paper, the higher-order singular value decomposition and the LU decomposition are applied to solve the general multi-linear systems, rather than special structure like M−tensor. Here, we transform the general tensor system into a form with a special structure. In addition, an iterative refinement method is constructed by the information of the coefficient tensor itself, the higher-order singular value, instead of the spectra of iterative tensor. Finally, the numerical experimental results are given to demonstrate the efficiency of the iterative refinement method.