# Two new eigenvalue localization sets for tensors and theirs applications

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1267-1276
- ISSN: 2391-5455

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topJianxing Zhao, and Caili Sang. "Two new eigenvalue localization sets for tensors and theirs applications." Open Mathematics 15.1 (2017): 1267-1276. <http://eudml.org/doc/288304>.

@article{JianxingZhao2017,

abstract = {A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1), 187-198). As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.},

author = {Jianxing Zhao, Caili Sang},

journal = {Open Mathematics},

keywords = {Nonnegative tensors; Tensor eigenvalue; Localization set; Positive definite; Spectral radius},

language = {eng},

number = {1},

pages = {1267-1276},

title = {Two new eigenvalue localization sets for tensors and theirs applications},

url = {http://eudml.org/doc/288304},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Jianxing Zhao

AU - Caili Sang

TI - Two new eigenvalue localization sets for tensors and theirs applications

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1267

EP - 1276

AB - A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50). As an application, a weaker checkable sufficient condition for the positive (semi-)definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1), 187-198). As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

LA - eng

KW - Nonnegative tensors; Tensor eigenvalue; Localization set; Positive definite; Spectral radius

UR - http://eudml.org/doc/288304

ER -

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