Some criteria for identifying strong ℋ $\mathcal {H}$ -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.…”

“…From the inequalities (11) and (12), we know that A is a strong M-tensor according to Theorem 8. However, inequalities (10) and (13) show that the tensor A in this example cannot be identified to be a strong M-tensor using Lemmas 7, 8, 10 and 12 in Li et al (2014b), Theorem 3.15 in Zhang et al (2014), Theorem 9 in Li et al (2015), Theorem 3.4 in Kannan et al (2015), Theorem 3 in Wang et al (2016) and Theorem 2.2 in Xu et al (2018). Additionally, Theorems 4 and 6 in Li et al (2017) cannot also identify the tensor A to be a strong M-tensor, and the specific verifications are omitted here.…”