A multipoint perturbation formula for eigenvalue problems
Mathematical Physics
2025-07-29 v2 Numerical Analysis
math.MP
Numerical Analysis
Spectral Theory
Quantum Physics
Abstract
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby operators are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a resolvent formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory.
Cite
@article{arxiv.2305.08151,
title = {A multipoint perturbation formula for eigenvalue problems},
author = {Geneviève Dusson and Louis Garrigue and Benjamin Stamm},
journal= {arXiv preprint arXiv:2305.08151},
year = {2025}
}