Skip to main content
SpringerLink
Log in

Criteria for strong H-tensors

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barmpoutis A, Vemuri B C, Howland D, Forder J R. Regularized positive-definite fourth order tensor field estimation from DW-MRI. Neuroimage, 2009, 45: 153–162

    Article  Google Scholar 

  2. Barmpoutis A, Vemuri B C, Shepherd T M, Forder J R. Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi. Transactions on Medical Imaging, 2007, 26: 1537–1546

    Article  Google Scholar 

  3. Basser P J, Jones D K. Diffusion-tensor MRI: theory, experimental design and data analysis—a technical review. NMR Biomed, 2002, 15: 456–467

    Article  Google Scholar 

  4. Basser P J, Mattiello J, Le Bihan D. Estimation of the effective self-diffusion tensor from the NMR spin echo. J Magn Reson B, 1994, 103: 247–254

    Article  Google Scholar 

  5. Brachat J, Comon P, Mourrain B, Tsigaridas E. Symmetric tensor decomposition. Linear Algebra Appl, 2010, 433: 1851–1872

    Article  MathSciNet  MATH  Google Scholar 

  6. Chang K, Pearson K, Zhang T. Perron-Frobenius theorem for nonnegative tensors. Commun Math Sci, 2008, 6: 507–520

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen H, Qi L. Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors. J Ind Manag Optim, 2015, 11: 1263–1274

    Article  MathSciNet  MATH  Google Scholar 

  8. Cichocki A, Zdunek R, Huy P, Amari S. Nonnegative Matrix and Tensor Factorizations. New York: John Wiley & Sons, Ltd, 2009

    Book  Google Scholar 

  9. De Lathauwer L, De Moor B, Vandewalle J. A multilinear singular value decomposition. SIAM J Matrix Anal Appl, 2010, 21: 1253–1278

    Article  MathSciNet  MATH  Google Scholar 

  10. Ding W, Qi L, Wei Y. M-tensors and nonsingular M-tensors. Linear Algebra Appl, 2013, 439: 3264–3278

    Article  MathSciNet  MATH  Google Scholar 

  11. Gandy S, Recht B, Yamada I. Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Problems, 2011, 27: 025010

    Article  MathSciNet  MATH  Google Scholar 

  12. Horn R A, Johnson C R. Matrix Analysis. Cambridge: Cambridge University Press, 1985

    Book  MATH  Google Scholar 

  13. Hu S, Huang Z, Qi L. Strictly nonnegative tensors and nonnegative tensor partition. Sci China Math, 2014, 57: 181–195

    Article  MathSciNet  MATH  Google Scholar 

  14. Kannan M R, Shaked-Monderer N, Berman A. Some properties of strong H-tensors and general H-tensors, Linear Algebra Appl, 2015, 476: 42–55

    Article  MathSciNet  MATH  Google Scholar 

  15. Kofidis E, Regalia P A. On the best rank-1 approximation of higher-order supersymmetric tensors, SIAM J Matrix Anal Appl, 2002, 23: 863–884

    Article  MathSciNet  MATH  Google Scholar 

  16. Kolda T G, Bader B W. Tensor decompositions and applications. SIAM Review, 2009, 51: 455–500

    Article  MathSciNet  MATH  Google Scholar 

  17. Li C, Wang F, Zhao J, Zhu Y, Li Y. Criterions for the positive definiteness of real supersymmetric tensors. J Comput Appl Math, 2014, 255: 1–14

    Article  MathSciNet  MATH  Google Scholar 

  18. Li Y, Liu Q, Qi L. Criteria for strong H-tensor. 2015, preprint

    Google Scholar 

  19. Nikias C L, Mendel J M. Signal processing with higher-order spectra. IEEE Signal Processing Magazine, 1993, 10: 10–37

    Article  Google Scholar 

  20. Qi L. Eigenvalues of a real supersymmetric tensor. J Symbolic Comput, 2005, 40: 1302–1324

    Article  MathSciNet  MATH  Google Scholar 

  21. Qi L, Yu G, Wu E X. Higher order positive semidefinite diffusion tensor imaging. SIAM J Imaging Sci, 2010, 3: 416–433

    Article  MathSciNet  MATH  Google Scholar 

  22. Qi L, Xu C, Xu Y. Nonnegative tensor factorization, completely positive tensors and a Hierarchically elimination algorithm. SIAM J Matrix Anal Appl, 2014, 35: 1227–1241

    Article  MathSciNet  MATH  Google Scholar 

  23. Song Y, Qi L. Infinite and finite dimensional Hilbert tensors. Linear Algebra Appl, 2014, 451: 1–14

    Article  MathSciNet  MATH  Google Scholar 

  24. Song Y, Qi L. Necessary and sufficient conditions for copositive tensors. Linear Multilinear Algebra, 2015, 63: 120–131

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang Y, Zhou G, Caccetta L. Nonsingular H-tensor and its criteria. J Ind Manag Optim, 2016, 12(4): 1173–1186

    Article  MathSciNet  Google Scholar 

  26. Yang Y, Yang Q. Further results for Perron-Frobenius theorem for nonnegative tensors. SIAM J Matrix Anal Appl, 2010, 31: 2517–2530

    Article  MathSciNet  MATH  Google Scholar 

  27. Zhang L, Qi L, Zhou G. M-tensors and some applications. SIAM J Matrix Anal Appl, 2014, 35: 437–452

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management Science, Qufu Normal University, Rizhao, 276800, China

    Yiju Wang & Kaili Zhang

  2. School of Science, Linyi University, Linyi, 276000, China

    Hongchun Sun

Authors
  1. Yiju Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kaili Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongchun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiju Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Zhang, K. & Sun, H. Criteria for strong H-tensors. Front. Math. China 11, 577–592 (2016). https://doi.org/10.1007/s11464-016-0525-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-016-0525-z

Keywords

MSC

Search

Navigation