Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension

Fabien Casenave 1 Alexandre Ern 2 Tony Lelièvre 2, 3
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.
Type de document :
Article dans une revue
Applied Mathematics Letters, Elsevier, 2016, 56, pp.23 - 28. 〈10.1016/j.aml.2015.11.010〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01186039
Contributeur : Fabien Casenave <>
Soumis le : lundi 24 août 2015 - 08:15:51
Dernière modification le : mercredi 19 décembre 2018 - 11:46:20

Lien texte intégral

Identifiants

Collections

Citation

Fabien Casenave, Alexandre Ern, Tony Lelièvre. Variants of the Empirical Interpolation Method: Symmetric formulation, choice of norms and rectangular extension. Applied Mathematics Letters, Elsevier, 2016, 56, pp.23 - 28. 〈10.1016/j.aml.2015.11.010〉. 〈hal-01186039〉

Partager

Métriques

Consultations de la notice

271