C-eigenvalues intervals for Piezoelectric-type tensors

TL;DR

This paper introduces two intervals to locate all C-eigenvalues of piezoelectric-type tensors, providing bounds for the largest eigenvalue, with numerical examples illustrating the results.

Contribution

The paper proposes a novel method to bound all C-eigenvalues of piezoelectric tensors, aiding in understanding their spectral properties.

Findings

Intervals effectively locate all C-eigenvalues

Upper bounds for the largest C-eigenvalue are established

Numerical examples validate the theoretical results

Abstract

C-eigenvalues of piezoelectric-type tensors which are real and always exist, are introduced by Chen et al. [1]. And the largest C-eigenvalue for the piezoelectric tensor determines the highest piezoelectric coupling constant. In this paper, we give two intervals to locate all C-eigenvalues for a given Piezoelectric-type tensor. These intervals provide upper bounds for the largest C-eigenvalue. Numerical examples are also given to show the corresponding results.