New practical criteria for ℋ-tensors and its application

Some Criteria for $${\varvec{\mathcal {H}}}$$-Tensors

“…In this paper, we establish some new criteria in identifying nonsingular H-tensors and give two numerical examples. These criteria are different from those of [1,6,7,9,10,12].…”

“…In [6,7], the authors provided an iterative algorithm for strong H-tensors, respectively. In [1,9,10,12], the authors gave some criteria for H-tensors. In [8], the authors gave some properties and conditions for H-tensors and nonsingular H-tensors.…”

“…The H-tensor which contains the M-tensor as special cases plays an important role in identifying positive definiteness of even-order real symmetric tensors [2,3,5,11]. In [1,6,7,9,10,12], the authors presented some criteria for H-tensors. In [8], the authors gave some properties and conditions for H-tensors and nonsingular H-tensors.…”

Some results on Brauer-type and Brualdi-type eigenvalue inclusion sets for tensors

“…These criteria can be used to identify strong M-tensor when a given tensor is a Z-tensor, but most of the existing sufficient conditions of strong H-tensor seem formally complex, and may verify to be a tedious task. Some of the detailed results on strong H-tensor can be found in Ding et al (2013), Kannan et al (2015), Li et al (2014bLi et al ( , 2017, Wang et al (2017a), Wang and Wei (2016), Wang et al (2016Wang et al ( , 2017b, Xu et al (2018), Zhang and Bu (2018). We next consider two numerical examples to show the applications of Theorems 8 and 9.…”

New iterative criteria for strong H $\mathcal{H}$ -tensors and an application

“…In this paper, we continue this research on criteria for strong -tensors; inspired by the ideas of [ 21 ], we obtain some new iterative criteria for strong -tensors, which improve the aforementioned Lemmas 1.3 - 1.6 . As applications of the new iterative criteria for strong -tensors, we establish some sufficient conditions of the positive definiteness for an even-order real symmetric tensor.…”