A new $(I+P)$-like preconditioner for the SOR method for solving multi-linear systems with $ \mathcal{M} $-tensors

The use of preconditioning techniques has been shown to offer significant advantages in solving multi-linear systems involving nonsingular $\mathcal{M}$-tensors. In this paper, we introduce a new preconditioner that employs $(I+P)$-like preconditioning techniques, and give the proof of its convergence. We also present numerical examples and comparison results that demonstrate the superior efficiency of our preconditioner compared to both the original SOR method and the previously proposed preconditioned SOR method.