Comparison theorems for nonnegative splittings of tensors

In this paper, by analogy with the definition of the nonnegative splitting of a matrix, we introduce the definition of the nonnegative splitting of a tensor. Considering the case that nonnegative splitting of a strong M-tensor is not necessarily convergent, we establish a new convergence theorem. Since comparison theorems involving the spectral radius of iterative tensors are useful tools in the analysis of convergence rate of tensor splitting iterative (TSI) methods, we derive several comparison theorems for nonnegative splittings of tensors in this paper. These results generalize the previous ones.