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01-12-2020 | Issue 4/2020

Calcolo 4/2020

Some improved Ky Fan type eigenvalue inclusion sets for tensors

Journal:
Calcolo > Issue 4/2020
Authors:
Yangyang Xu, Bing Zheng, Ruijuan Zhao
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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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