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

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Abstract

Strong \(\mathcal {H}\)-tensors play an important role in identifying positive semidefiniteness of even-order real symmetric tensors. We provide several simple practical criteria for identifying strong \(\mathcal {H}\)-tensors. These criteria only depend on the elements of the tensors; therefore, they are easy to be verified. Meanwhile, a sufficient and necessary condition of strong \(\mathcal {H}\)-tensors is obtained. We also propose an algorithm for identifying the strong \(\mathcal {H}\)-tensors based on these criterions. Some numerical results show the feasibility and effectiveness of the algorithm.

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Acknowledgments

This work was supported by the Hong Kong Research Grant Council (grant number PolyU 502510, 502111, 501212 and 501913) and the first author was supported by the National Natural Science Foundations of China (11361074).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, 650091, Kunming, Yunnan, People’s Republic of China

    Yaotang Li & Qilong Liu

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

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  1. Yaotang Li
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  2. Qilong Liu
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  3. Liqun Qi
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Correspondence to Yaotang Li.

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Li, Y., Liu, Q. & Qi, L. Programmable criteria for strong \(\mathcal {H}\)-tensors. Numer Algor 74, 199–221 (2017). https://doi.org/10.1007/s11075-016-0145-4

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