A new S-type eigenvalue localization set for tensors and its applications
Abstract
A new \emph{S}-type eigenvalue localization set for tensors is derived by breaking into disjoint subsets and its complement. It is proved that this new set is tighter than those presented by Qi (Journal of Symbolic Computation 40 (2005) 1302-1324), Li et al. (Numer. Linear Algebra Appl. 21 (2014) 39-50) and Li et al. (Linear Algebra Appl. 493 (2016) 469-483). As applications, checkable sufficient conditions for the positive definiteness and the positive semi-definiteness of tensors are proposed. Moreover, based on this new set, we establish a new upper bound for the spectral radius of nonnegative tensors and a lower bound for the minimum \emph{H}-eigenvalue of weakly irreducible strong \emph{M}-tensors in this paper. We demonstrate that these bounds are sharper than those obtained by Li et al. (Numer. Linear Algebra Appl. 21 (2014) 39-50) and He and Huang (J. Inequal. Appl. 114 (2014) 2014). Numerical examples are also given to illustrate this fact.
Keywords
Cite
@article{arxiv.1602.07568,
title = {A new S-type eigenvalue localization set for tensors and its applications},
author = {Zhengge Huang and Ligong Wang and Zhong Xu and Jingjing Cui},
journal= {arXiv preprint arXiv:1602.07568},
year = {2016}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:1510.05207 by other authors