Abstract
To locate the eigenvalues of a given tensor, we present two classes of new Ky Fan type eigenvalue inclusion sets for tensors, which are tighter than those in Yang et al. (SIAM J Matrix Anal Appl 31:2517–2530, 2010) and He et al. (J Inequal Appl 114:1-9, 2014), respectively. Under certain conditions, the theoretical comparisons of the new proposed Ky Fan type eigenvalue inclusion sets for tensors are established. As applications, some sufficient conditions for identifying strong \(\mathcal {M}\)-tensors, the non-singularity and positive definiteness of tensors are obtained. Some numerical examples are given to verify the validity of our theoretical results.
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Acknowledgements
The authors would like to thank the anonymous referees who made much useful and detailed suggestions that helped us to improve the quality of this paper. This work was supported by the Young Scholars Science Foundation of Lanzhou Jiaotong University (No. 2020025), the National Natural Science Foundation of China (No. 11571004) and the Fundamental Research Funds for the Central Universities (No. lzujbky-2017-it54).
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Xu, Y., Zheng, B. & Zhao, R. Some improved Ky Fan type eigenvalue inclusion sets for tensors. Calcolo 57, 40 (2020). https://doi.org/10.1007/s10092-020-00389-z
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DOI: https://doi.org/10.1007/s10092-020-00389-z