Preconditioned iterative methods for multi-linear systems based on the majorization matrix

Abstract

This paper mainly deals with applying a general class of preconditioners to accelerate the convergence speed of some iterative schemes for solving multi-linear systems whose coefficient tensors are strong -tensors. Theoretical results are established to analyse the performance of a general class of preconditioners extracted from the majorization matrix associated with the coefficient tensor. Brief discussions are included in using a Krylov subspace method based on the Hessenberg process to solve the mentioned problem. For the sake of generality, we consider multi-linear systems with multiple right-hand sides. Numerical experiments are reported to illustrate the validity of the presented theoretical results.