Improving the Gauss–Seidel iterative method for solving multi-linear systems with $$\mathcal {M}$$ -tensors

Abstract

The main objective of this paper is to solve multi-linear systems with strong \( \mathcal {M}\)-tensors using preconditioned methods based on tensor splitting. In this paper, we propose a new preconditioned Gauss–Seidel iterative method for solving multi-linear systems. The convergence and comparison theorems of the proposed method are discussed. Finally, some numerical experiments are given to confirm our theoretical analysis and demonstrate the efficiency of the proposed method.