An optimal Z-eigenvalue inclusion interval for a sixth-order tensor and its an application

Abstract

An optimal Z-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.

Keywords

• sixth-order tensors
• z-eigenvalues
• inclusion intervals
• positive definiteness