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Calcolo
Published in: Calcolo 4/2020

01-12-2020

Some improved Ky Fan type eigenvalue inclusion sets for tensors

Authors: Yangyang Xu, Bing Zheng, Ruijuan Zhao

Published in: Calcolo | Issue 4/2020

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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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Metadata
Title
Some improved Ky Fan type eigenvalue inclusion sets for tensors
Authors
Yangyang Xu
Bing Zheng
Ruijuan Zhao
Publication date
01-12-2020
Publisher
Springer International Publishing
Published in
Calcolo / Issue 4/2020
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-020-00389-z

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