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dc.contributor.authorBinev, Peter
dc.contributor.authorCohen, Albert
dc.contributor.authorMula, Olga
dc.contributor.authorNichols, James
dc.date.accessioned2019-09-16T13:38:45Z
dc.date.available2019-09-16T13:38:45Z
dc.date.issued2018
dc.identifier.issn2166-2525
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19808
dc.language.isoenen
dc.subjectgreedy algorithmsen
dc.subjectdata assimilationen
dc.subjectreduced modelsen
dc.subjectsensor placementen
dc.subjectinf-sup stabilityen
dc.subject.ddc515en
dc.titleGreedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Modelsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the problem of optimal recovery of an unknown function u in a Hilbert space V from measurements of the form j (u), j = 1,. .. , m, where the j are known linear functionals on V. We are motivated by the setting where u is a solution to a PDE with some unknown parameters , therefore lying on a certain manifold contained in V. Following the approach adopted in [9, 3], the prior on the unknown function can be described in terms of its approximability by finite-dimensional reduced model spaces (V n) n≥1 where dim(V n) = n. Examples of such spaces include classical approximation spaces, e.g. finite elements or trigonometric polynomials, as well as reduced basis spaces which are designed to match the solution manifold more closely. The error bounds for optimal recovery under such priors are of the form µ(V n , W m)ε n , where ε n is the accuracy of the reduced model V n and µ(V n , W m) is the inverse of an inf-sup constant that describe the angle between V n and the space W m spanned by the Riesz representers of (1 ,. .. , m). This paper addresses the problem of properly selecting the measurement func-tionals, in order to control at best the stability constant µ(V n , W m), for a given reduced model space V n. Assuming that the j can be picked from a given dictionary D we introduce and analyze greedy algorithms that perform a sub-optimal selection in reasonable computational time. We study the particular case of dictionaries that consist either of point value evaluations or local averages, as idealized models for sensors in physical systems. Our theoretical analysis and greedy algorithms may therefore be used in order to optimize the position of such sensors.en
dc.relation.isversionofjnlnameSIAM/ASA Journal on Uncertainty Quantification
dc.relation.isversionofjnlvol6en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2018-08
dc.relation.isversionofjnlpages1101-1126en
dc.relation.isversionofdoi10.1137/17M1157635en
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematicsen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-09-16T13:35:47Z
hal.person.labIds106904
hal.person.labIds25
hal.person.labIds60
hal.person.labIds25


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