Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation
For researchers in tensor eigenvalue computation, this provides a tighter inclusion set but is an incremental extension of existing Gersgorin-type results.
The paper defines the Minimal Gersgorin tensor eigenvalue inclusion set for complex tensors, provides its necessary and sufficient condition, and studies its boundary using equimodular sets. A numerical approximation method is given for irreducible tensors.
For a complex tensor A, Minimal Gersgorin tensor eigenvalue inclusion set of A is presented, and its sufficient and necessary condition is given. Furthermore, we study its boundary by the spectrums of the equimodular set and the extended equimodular set for A. Lastly, for an irreducible tensor, a numerical approximation to Minimal Gersgorin tensor eigenvalue inclusion set is given.