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

Zheng Ge Huang; Li Gong Wang; Zhong Xu; Jing Jing Cui

doi:10.1186/s13660-016-1200-3

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

Zheng Ge Huang, Li Gong Wang, Zhong Xu, Jing Jing Cui

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N= { 1 , 2 , … , n} 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).

Original language	English
Article number	254
Journal	Journal of Inequalities and Applications
Volume	2016
Issue number	1
DOIs	https://doi.org/10.1186/s13660-016-1200-3
State	Published - 1 Dec 2016

Keywords

minimum H-eigenvalue
nonnegative tensor
nonsingular M-tensor
positive definite
spectral radius
tensor eigenvalue

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10.1186/s13660-016-1200-3

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abstract = "In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N= { 1 , 2 , … , n} 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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AU - Wang, Li Gong

AU - Xu, Zhong

AU - Cui, Jing Jing

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Y1 - 2016/12/1

N2 - In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N= { 1 , 2 , … , n} 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).

AB - In this paper, a new S-type eigenvalue localization set for a tensor is derived by dividing N= { 1 , 2 , … , n} 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).

KW - minimum H-eigenvalue

KW - nonnegative tensor

KW - nonsingular M-tensor

KW - positive definite

KW - spectral radius

KW - tensor eigenvalue

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

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Keywords

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