A tighter $Z$-eigenvalue localization set for tensors and its applications
Provides an incremental improvement in eigenvalue localization for tensor analysis, benefiting researchers in tensor computation and related fields.
The paper proposes a tighter Z-eigenvalue localization set for tensors, which improves upon previous bounds, and derives a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors, with numerical verification.
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.