Some bounds for H-eigenpairs and Z-eigenpairs of a tensor

摘要

In this paper, we consider the H-eigenpairs and Z-eigenpairs of a tensor. By estimating the ratio of the smallest and largest entries in the Perron vector, we present some sharper bounds for the H-spectral radius of a nonnegative irreducible tensor. Similarly, we also obtain some Z-spectral radius bounds of an irreducible weakly symmetric tensor. In addition, by using the technique of matricizing, several bounds for the Z-spectrum are derived. These proposed bounds improve some existing ones, and some numerical examples are given to show the theoretical results.