Tensor splitting preconditioners for multilinear systems

In this paper, we propose some new preconditioners  for solving multilinear system \mathcal{A}\mathbf{x}^{m-۱}=\mathbf{b}. These preconditioners are based on tensor splitting. We also present some theorems for analyzing and convergence of the preconditioned  Jacobi-, Gauss-Seidel-, and SOR-type iterative methods. Numerical examples are presented to verify the efficiency of the proposed preconditioned methods.

Keywords:

Multilinear system , \mathcal{M}-tensor , tensor splitting , preconditioned methods