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.
@article{bwmeta1.element.doi-10_1515_math-2017-0106,
author = {Jianxing Zhao and Caili Sang},
title = {Two new eigenvalue localization sets for tensors and theirs applications},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1267-1276},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0106}
}
Jianxing Zhao; Caili Sang. Two new eigenvalue localization sets for tensors and theirs applications. Open Mathematics, Tome 15 (2017) pp. 1267-1276. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0106/