Two new eigenvalue localization sets for tensors and theirs applications

Jianxing 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 -