Some criteria for identifying strong \(\mathcal {H}\)-tensors

  • Yangyang Xu
  • Ruijuan Zhao
  • Bing Zheng
Original Paper


In this paper, we present some new criteria only depending on the elements of the given tensors for judging strong \(\mathcal {H}\)-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 \(\mathcal {H}\)-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.


Strong \(\mathcal {H}\)-tensors Criteria Multivariate form Positive definiteness 


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The authors would like to thank two anonymous referees for their valuable suggestions and constructive comments that improved the quality of this paper.

Funding information

This work was supported by the Natural Science Foundation of China (No. 11571004) and the Fundamental Research Funds for the Central Universities (lzujbky-2017-it54).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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