Richardson Iterative Method for Solving Multi-Linear System with M-Tensor

In this paper, Richardson iterative method is employed to solve M-Equation. In order to guaran-tee the solution can be found, convergence theorems are established and confirmed numerically. The optimal a, which is a parameter of Richardson iterative method that can provide the best convergence rate, is also determined theoretically and numerically. Furthermore, a theorem es-tablishing the range of initial vector for general splitting methods is extended from the range in past study. To further accelerate the convergence rate, Anderson accelerator and three precon-ditioners are incorporated into Richardson iterative method. Numerical results reveal that by including these accelerators, the convergence rates are enhanced. Finally, we show that Richard-son iterative methods with optimal a perform better than the SOR type methods in past studies in terms of number of iterative steps and CPU time.