In this paper, we propose some new preconditioners for solving multilinear system $\mathcal{A}\mathbf{x}^{m-1}=\mathbf{b}$. 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.
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