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Two non-parameter iterative algorithms for identifying strong \(\mathcal {H}\)-tensors

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Abstract

The strong \(\mathcal {H}\)-tensors have important applications in many areas of science and engineering, e.g., the determination of positive definiteness for an even-order homogeneous polynomial form in the real field. In this paper, we propose two iterative algorithms with non-parameter for identifying strong \(\mathcal {H}\)-tensors, which overcome the drawback of choosing the best value of parameter 𝜖 in some existing algorithms given by Li et al. and Liu et al. (J. Comput. Appl. Math., 255, 1–14, 2014 and Comput. Appl. Math. 36, 1623–1635, 2017). Some numerical experiments are performed to illustrate the feasibility and effectiveness of our algorithms.

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Funding

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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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Yangyang Xu, Ruijuan Zhao & Bing Zheng

Authors
  1. Yangyang Xu
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  2. Ruijuan Zhao
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  3. Bing Zheng
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Correspondence to Bing Zheng.

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Xu, Y., Zhao, R. & Zheng, B. Two non-parameter iterative algorithms for identifying strong \(\mathcal {H}\)-tensors. Numer Algor 81, 1113–1128 (2019). https://doi.org/10.1007/s11075-018-0587-y

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  • DOI: https://doi.org/10.1007/s11075-018-0587-y

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