| Issue |
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
|
|
|---|---|---|
| Page(s) | 2081 - 2109 | |
| DOI | https://doi.org/10.1051/m2an/2025048 | |
| Published online | 24 July 2025 | |
A multipoint perturbation formula for eigenvalue problems
1
Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France
2
Laboratoire “analyse géométrie modélisation”, CY Cergy Paris Université, 95302 Cergy-Pontoise, France
3
Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, 70569 Stuttgart, Germany
* Corresponding author: louis.garrigue@cyu.fr
Received:
30
April
2024
Accepted:
14
June
2025
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.
Mathematics Subject Classification: 47Axx / 47A55 / 47A75
Key words: Eigenvalue problem / approximation of solutions / perturbation theory / interpolation
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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