A new preconditioned AOR method for solving multi-linear systems

ABSTRACT

In this paper, a new preconditioned AOR method for solving the multi-linear systems with $\mathcal{M}$-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.

KEYWORDS:

• Multi-linear systems
• preconditioned AOR method
• strong $\mathcal{M}$-tensor
• higher order Markov chain

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 15A72
• 65N12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Natural Science Foundation of China [grant number 12161027], Guangxi Natural Science Foundation [grant number 2020GXNSFAA159143], and Guilin University of Electronic Technology [grant number 2021YCXS114].