In this paper, we propose some new preconditioners for solving multilinear system Ax^ {m−1} = b. These preconditioners are based on tensor splitting. We also present some theorems for analyzing and converging the preconditioned Jacobi, Gauss-Seidel, and SOR-type iterative methods. Numerical examples are presented to verify the efficiency of the proposed preconditioned methods.
Mathematics Subject Classification (2010). 15A10, 15A69, 15A72, 15A99, 65F10.