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E-eigenvalue Localization Sets for Fourth-Order Tensors

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Abstract

A Geršgorin-type E-eigenvalue localization set and two Brauer-type E-eigenvalue localization sets for fourth-order tensors are presented. As applications, some sufficient conditions for the positive (semi-)definiteness of fourth-order real symmetric tensors and some upper bounds for the Z-spectral radius of fourth-order weakly symmetric nonnegative tensors are obtained. Finally, numerical examples are given to verify the theoretical results.

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Acknowledgements

The author is grateful to the referees and Editor-in-Chief Prof. Rosihan M. Ali for their comments and suggestions. This work is supported by National Natural Science Foundations of China (Grant No. 11501141); Science and Technology Top-notch Talents Support Project of Education Department of Guizhou Province (Grant No. QJHKYZ [2016]066); CAS ‘Light of West China’ Program.

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Authors and Affiliations

  1. College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, People’s Republic of China

    Jianxing Zhao

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Jianxing Zhao

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  1. Jianxing Zhao
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Correspondence to Jianxing Zhao.

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Fuad Kittaneh.

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Zhao, J. E-eigenvalue Localization Sets for Fourth-Order Tensors. Bull. Malays. Math. Sci. Soc. 43, 1685–1707 (2020). https://doi.org/10.1007/s40840-019-00768-y

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  • DOI: https://doi.org/10.1007/s40840-019-00768-y

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