A new preconditioned AOR method for solving multi-linear systems.

In this paper, a new preconditioned AOR method for solving the multi-linear systems with $ \mathcal {M} $ M -tensor is presented. The convergence of the new method and the corresponding comparison for the spectral radius of preconditioned iterative tensors are given. Numerical examples demonstrate that the new method is feasible and effective. As an application, we also show the efficiency of our preconditioner for solving higher order Markov chains. [ABSTRACT FROM AUTHOR]