{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-multipoint-perturbation-formula-for","title":"A multipoint perturbation formula for eigenvalue problems","arxiv_id":"2305.08151","date":"2023-05-14","proceeding":null,"authors":["Geneviève Dusson","Louis Garrigue","Benjamin Stamm"],"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.","url_abs":"https://arxiv.org/abs/2305.08151v1","url_pdf":"https://arxiv.org/pdf/2305.08151v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-multipoint-perturbation-formula-for","repo_url":"https://github.com/lgarrigue/multipoint_perturbation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}