Some criteria for identifying strong -tensors and its applications

Abstract

In this paper, we establish some criteria for strong $\mathcal{H}$-tensors. The results obtained in this paper extend the corresponding conclusions for strong $\mathcal{H}$-matrices and improve the existing results for strong $\mathcal{H}$-tensors. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are presented. Some numerical results show the feasibility and effectiveness of the results which are obtained in this paper.

Keywords:

• Strong $\mathcal{H}$-tensors
• iterative criteria
• positive definiteness
• homogeneous polynomial
• strictly diagonally dominant

AMS Subject Classifications:

• 15A69
• 15A18
• 65F15
• 65H17

Acknowledgements

The authors are grateful to the anonymous referees for their useful suggestions and comments that improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by National Science Foundation of China [grant number 41725017]; National Basic Research Program of China [grant number 2014CB845906]. It is also partially supported by the CAS/CAFEA international partnership Program for creative research teams [grant number KZZD-EW-TZ-19], [grant number KZZD-EW-TZ-15]; Strategic Priority Research Program of the Chinese Academy of Sciences [grant number XDB18010202] and Fujian Natural Science Foundation [grant number 2016J01005].