Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation

TL;DR

This paper introduces the minimal Gersgorin tensor eigenvalue inclusion set for complex tensors, characterizes its boundary, and provides a numerical approximation method for irreducible tensors, advancing tensor eigenvalue analysis.

Contribution

It defines the minimal Gersgorin tensor eigenvalue inclusion set, establishes its necessary and sufficient conditions, and offers a numerical approximation approach for irreducible tensors.

Findings

Characterization of the boundary via spectrums of equimodular sets

Necessary and sufficient conditions for the inclusion set

Numerical approximation method for irreducible tensors

Abstract

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.