A new $Z$-eigenvalue inclusion theorem for tensors
For researchers in tensor eigenvalue theory, this provides an incremental improvement in bounding Z-eigenvalues and spectral radii.
The paper presents a new Z-eigenvalue inclusion theorem for tensors that is tighter than existing ones, leading to a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors, with numerical examples demonstrating effectiveness.
A new $Z$-eigenvalue inclusion theorem for tensors is given and proved to be tighter than those in [G. Wang, G.L. Zhou, L. Caccetta, $Z$-eigenvalue inclusion theorems for tensors, Discrete and Continuous Dynamical Systems Series B,22(1) (2017) 187--198]. Based on this set, a sharper upper bound for the $Z$-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to show the effectiveness of the proposed bound.