Numerical Algorithms

, Volume 81, Issue 3, pp 1113–1128 | Cite as

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

  • Yangyang Xu
  • Ruijuan Zhao
  • Bing ZhengEmail author
Original Paper


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.


Strong \(\mathcal {H}\)-tensors Non-parameter Iterative algorithm Positive definiteness 

Mathematics Subject Classification (2010)

15A18 15A69 


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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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Copyright information

© 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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