Some criteria for identifying strong H-tensors

摘要

In this paper, we present some new criteria only depending on the elements of the given tensors for judging strong H-tensors which cannot be identified by some existing criteria in Li et al. (J. Comput. Appl. Math. 255, 1-4, 2014) and Zhao et al. (Front. Math. China 11, 661-678, 2016). Some new necessary and sufficient conditions of strong H-tensors are also provided. As an application, some sufficient conditions for identifying the positive definiteness of a class of multivariate forms are obtained. These facts are well illustrated by some numerical examples.