Nonlinear eigenvalue approximation for compact operators

TL;DR

This paper extends spectral approximation theory for compact operators to nonlinear eigenvalue problems, providing new insights and correction terms, with applications demonstrated in electromagnetics.

Contribution

It introduces a novel extension of spectral approximation theory to nonlinear eigenvalue problems, including correction terms and practical electromagnetic applications.

Findings

Extended spectral approximation theory to nonlinear eigenvalue problems.

Provided first-order correction terms for improved eigenvalue approximation.

Demonstrated applications in electromagnetics.

Abstract

In \cite{Os} a general spectral approximation theory was developed for compact operators on a Banach space which does not require that the operators be self-adjoint and also provides a first order correction term. Here we extend some of the results of that paper to nonlinear eigenvalue problems. We present examples of its application that arise in electromagnetics.