Mehdi Najafi-Kalyani - Department of Mathematics, Vali-e-Asr University of Rafsanjan, PO Box ۵۱۸, Rafsanjan, Iran
Fatemeh P. A. Beik - Department of Mathematics, Vali-e-Asr University of Rafsanjan, PO Box ۵۱۸, Rafsanjan, Iran

Recently, Zhang et al. [Applied Mathematics Letters ۱۰۴ (۲۰۲۰) ۱۰۶۲۸۷] proposed a preconditioner to improve the convergence speed of three types of Jacobi iterative methods for solving multi-linear systems. In this paper, we consider the Jacobi-type method which works better than the other two ones and apply a new preconditioner. The convergence of proposed preconditioned iterative method is studied. It is shown that the new approach is superior to the recently examined one in the literature. Numerical experiments illustrate the validity of theoretical results and the efficiency of the proposed preconditioner.

Iterative method, multi-linear system, strong mathcal{M}-tensor, preconditioning