A new S-type eigenvalue inclusion set for tensors and its applications

In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra App...

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Autores principales: Huang, Zheng-Ge, Wang, Li-Gong, Xu, Zhong, Cui, Jing-Jing
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5181102/
https://www.ncbi.nlm.nih.gov/pubmed/28077920
http://dx.doi.org/10.1186/s13660-016-1200-3
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author Huang, Zheng-Ge
Wang, Li-Gong
Xu, Zhong
Cui, Jing-Jing
author_facet Huang, Zheng-Ge
Wang, Li-Gong
Xu, Zhong
Cui, Jing-Jing
author_sort Huang, Zheng-Ge
collection PubMed
description In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of strong M-tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).
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spelling pubmed-51811022017-01-09 A new S-type eigenvalue inclusion set for tensors and its applications Huang, Zheng-Ge Wang, Li-Gong Xu, Zhong Cui, Jing-Jing J Inequal Appl Research In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of strong M-tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014). Springer International Publishing 2016-10-19 2016 /pmc/articles/PMC5181102/ /pubmed/28077920 http://dx.doi.org/10.1186/s13660-016-1200-3 Text en © Huang et al. 2016 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Huang, Zheng-Ge
Wang, Li-Gong
Xu, Zhong
Cui, Jing-Jing
A new S-type eigenvalue inclusion set for tensors and its applications
title A new S-type eigenvalue inclusion set for tensors and its applications
title_full A new S-type eigenvalue inclusion set for tensors and its applications
title_fullStr A new S-type eigenvalue inclusion set for tensors and its applications
title_full_unstemmed A new S-type eigenvalue inclusion set for tensors and its applications
title_short A new S-type eigenvalue inclusion set for tensors and its applications
title_sort new s-type eigenvalue inclusion set for tensors and its applications
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5181102/
https://www.ncbi.nlm.nih.gov/pubmed/28077920
http://dx.doi.org/10.1186/s13660-016-1200-3
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