Perturbation bounds for the largest C-eigenvalue of piezoelectric-type tensors

TL;DR

This paper analyzes how small changes in piezoelectric-type tensors affect their largest C-eigenvalue, which is crucial for understanding the maximum piezoelectric coupling, and introduces three bounds with high accuracy for small perturbations.

Contribution

The paper introduces three new perturbation bounds for the largest C-eigenvalue of piezoelectric tensors, with a focus on the accuracy of the third bound for small perturbations.

Findings

The third perturbation bound is highly accurate for small perturbations.

Theoretical analysis supports the effectiveness of the bounds.

Numerical examples demonstrate practical applicability.

Abstract

In this paper, we focus on the perturbation analysis of the largest C-eigenvalue of the piezoelectric-type tensor which has concrete physical meaning which determines the highest piezoelectric coupling constant. Three perturbation bounds are presented, theoretical analysis and numerical examples show that the third perturbation bound has high accuracy when the norm of the perturbation tensor is small.