A sorting algorithm for complex eigenvalues

TL;DR

This paper introduces SPEC-RE, a novel algorithm for sorting complex eigenvalues that depend analytically on parameters, effectively handling cases where existing methods fail, with applications in physics and engineering.

Contribution

The paper presents a new algorithm, SPEC-RE, for sorting complex eigenvalues with analytic parameter dependence, addressing limitations of previous methods.

Findings

Successfully sorts eigenvalues in complex parameter spaces

Handles cases where other methods fail

Demonstrates effectiveness through multiple examples

Abstract

We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are analytic functions of the parameters, with atmost algebraic singularities, is used in formulating the algorithm. Several examples are presented to demonstrate the efficacy of the method; simple examples where other methods fail are also presented. The algorithm is likely to be useful in several problems of physics and engineering that require identification and sorting of eigenmodes.