This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about preconditioned Jacobi, Gauss-Seidel and SOR type iterative methods. The main results theoretically prove that the preconditioners can accelerate the convergence of iterations. Numerical examples are presented to reverify the efficiency of the proposed preconditioned methods.

翻译：本文件调查了一种快速灵活的先决条件,用$\mathcal{M}$-tensor$\mthcal{A}解决多线性系统 $\mathcal{Gaus-Seidel 和 SOR 类型迭代方法的快速灵活前提。主要结果在理论上证明先决条件可以加速迭代的趋同。 提供了数字示例,以重新验证拟议先决条件方法的效率。