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Variants of the empirical interpolation method: symmetric formulation, choice of norms and rectangular extension / Fabien Casenave in Applied Mathematics Letters, vol 56 (June 2016)  

Public [article]  inApplied Mathematics Letters > vol 56 (June 2016) . - pp Titre : Variants of the empirical interpolation method: symmetric formulation, choice of norms and rectangular extension Type de document : Article/Communication Auteurs : Fabien Casenave , Auteur ; Alexandre Ern, Auteur ; Tony Lelièvre, Auteur Année de publication : 2016 Article en page(s) : pp Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Analyse numérique [Termes IGN] approximation [Termes IGN] interpolation Résumé : (auteur) 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. Numéro de notice : A2016--173 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : MATHEMATIQUE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1016/j.aml.2015.11.010 Date de publication en ligne : 07/12/2015 En ligne : https://doi.org/10.1016/j.aml.2015.11.010 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=91780 [article]