On the effective secular equation

TL;DR

This paper demonstrates that the effective secular equation is effective for estimating the positions of exceptional points in eigenvalue problems, using Mathieu equations as a key example.

Contribution

It validates the use of the effective secular equation for locating exceptional points, providing a practical approach for eigenvalue analysis.

Findings

Effective secular equation accurately estimates exceptional points.

Application to Mathieu equations confirms the method's utility.

Provides a foundation for analyzing non-Hermitian eigenvalue problems.

Abstract

We show that the effective secular equation proposed several years ago is suitable for estimating the location of the exceptional points of eigenvalue equations. As an illustrative example we choose the well known Mathieu