Adaptive approximation of nonlinear eigenproblems by minimal rational interpolation

Abstract: We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector‐valued function, defined as solution of a non‐homogeneous version of the eigenproblem. This approximation step is carried out via the minimal rational interpolation method. Notably, an adaptive sampling approach is employed: the expensive data needed for the approximation is gathered at locations that are optimally chosen by following a greedy error indicator. This allows the algorithm to employ computational resources only where where “most of the information” on not‐yet‐approximated eigenvalues can be found. Then, through a post‐processing of the surrogate, the sought‐after eigenvalues and eigenvectors are recovered. Numerical examples are used to showcase the effectiveness of the method.

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Adaptive approximation of nonlinear eigenproblems by minimal rational interpolation ; volume:22 ; number:1 ; year:2023 ; extent:0 ; Proceedings in applied mathematics and mechanics ; 22, Heft 1 (2023) (gesamt 0)

Beteiligte, Orts- und Zeitangaben

• Urheber: Pradovera, Davide

Weitere Informationen

• DOI: 10.1002/pamm.202200032
• URN: urn:nbn:de:101:1-2023032514083326825125
• Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 14.08.2025, 10:59 MESZ