A tighter $Z$-eigenvalue localization set for tensors and its applications

Abstract

A new $Z$-eigenvalue localization set for tensors is given and proved to be tighter than those presented by Wang \emph{et al}. (Discrete and Continuous Dynamical Systems Series B 22(1): 187-198, 2017) and Zhao (J. Inequal. Appl., to appear, 2017). As an application, a sharper upper bound for the $Z$-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

arXiv commentIn fact, this manuscript had been finished at 18th March, 2017. 12 pages. 1 figure. Comments and suggestions are highly welcome