Numerische Mathematik

, Volume 130, Issue 2, pp 315–335 | Cite as

Some bounds for the spectral radius of nonnegative tensors

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Abstract

In this paper, we extend the well-known column sum bound of the spectral radius for nonnegative matrices to the tensor case, an upper bound of the spectral radius for a nonnegative tensor is given via the largest eigenvalue of a symmetric tensor. Also we show some bounds of spectral radius of nonnegative tensors based on the sum of the entries in the other indices of tensors. We demonstrate that our new results improve existing results. The other main results of this paper is to provide a sharper Ky Fan type theorem and a comparison theorem for nonnegative tensors. Finally, we make use of our bounds to give a perturbation bound for the spectral radius of symmetric nonnegative tensors. This result is similar to the Weyl theorem for the matrix case.

Mathematics Subject Classification

15A18 15A69 65F25 
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Notes

Acknowledgments

We are thankful to referees for their valuable suggestions. Also we would like to thank Prof. Liqun Qi for sending us his recent paper [19] and some suggestions, and Prof. Chi-Kwong Li for the discussion when he visited Hong Kong Baptist University.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPeople’s Republic of China
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloonHong Kong
  3. 3.Hong Kong Baptist University Institute of Research and Continuing EducationShenzhenChina

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