A New Preconditioner of the Accelerated Over-Relaxation Iterative Method for Multi-Linear Systems

Multi-linear systems with Z-tensors are more general than those with M-tensors. In this paper, we consider multi-linear systems with Z-tensor coefficients. Theoretically, we provide a convergence analysis and compare the spectral radii of the preconditioned iteration tensor and the original tensor within the Z-tensor framework. Numerical examples are presented to verify the theoretical spectral radius comparisons. Additionally, numerical examples on nonsingular M-tensors demonstrate the effectiveness of the proposed preconditioner.