H-eigenvalue Inclusion Sets for Sparse Tensors

Sparse tensors play fundamental roles in hypergraph data, sensor node network data and remote sensing data. In this paper, we establish new H-eigenvalue inclusion sets for sparse tensors by their majorization matrix's digraph and representation matrix's digraph. Numerical examples are proposed to verify that our conclusions are more accurate and less computations than existing results. As applications, we provide some checkable sufficient conditions for the positive definiteness of even-order sparse tensors, and propose lower and upper bounds of H-spectral radius of nonnegative sparse tensors.