Filomat 2018 Volume 32, Issue 11, Pages: 3899-3916
https://doi.org/10.2298/FIL1811899H
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Some new inclusion sets for eigenvalues of tensors with application
Huang Zhengge
Wang Ligong
Xu Zhong
Cui Jingjing
In this paper, we are concerned with the eigenvalue inclusion sets for
tensors. Some new S-type eigenvalue localization sets for tensors are
employed by dividing N = {1,2,..., n} into disjoint subsets S and its
complement. Our new sets, are proved to be tighter than that newly derived
by Huang et al. (J. Inequal. Appl. 2016 (2016) 254). As applications, we can
apply the proposed sets for determining the positive (semi-)definiteness of
even-order symmetric tensors. Some examples are given to show the sharpness
of our new sets in contrast with the known ones, and verify the effectiveness
of those in identifying the positive (semi-)definiteness of tensors.
Keywords: tensor eigenvalue, inclusion set, positive definite, positive semi-definite