MODIFIED SPLITTING METHODS FOR SOLVING NON-HOMOGENOUS MULTI-LINEAR EQUATIONS WITH M-TENSORS

摘要

In this paper, we concern with solving non-homogenous multi-linear equations with M-tensors. We prove the existence and uniqueness of the positive solution to a non-homogenous M-tensor equation with a positive right-hand side vector. In addition, we expand some classical splitting methods like the Jacobi-like, Gauss-Seidel-like, simplified Gauss-Seidel-like, and SOR-like methods to solve the tensor equations, further providing their convergence analyses. Moreover, numerical results show that generally, the SOR-like method performs the best in iteration steps. The Jacobi-like method is the worst but requires less CPU time, and the effects of the other methods are between the above two with narrow distinctions in most non-sparse cases. Furthermore, the SOR-like method for the sparse cases needs the least CPU time, while the Jacobi-like method needs the most.