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dc.contributor.authorBergou, El Houcine
dc.contributor.authorGratton, Serge
dc.contributor.authorMandel, Jan
dc.date.accessioned2018-12-23T08:10:16Z
dc.date.available2018-12-23T08:10:16Z
dc.date.issued2018-11-29
dc.identifier.citationBergou EH, Gratton S, Mandel J (2019) On the convergence of a non-linear ensemble Kalman smoother. Applied Numerical Mathematics 137: 151–168. Available: http://dx.doi.org/10.1016/j.apnum.2018.11.008.
dc.identifier.issn0168-9274
dc.identifier.doi10.1016/j.apnum.2018.11.008
dc.identifier.urihttp://hdl.handle.net/10754/630346
dc.description.abstractEnsemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.
dc.description.sponsorshipPartially supported by the U.S. National Science Foundation under the grant DMS-1216481, the Czech Science Foundation under the grant 13-34856S and the Fondation STAE project ADTAO.
dc.publisherElsevier BV
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S0168927418302575
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Applied Numerical Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Numerical Mathematics, 29 November 2018. DOI: 10.1016/j.apnum.2018.11.008. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectEnsemble Kalman filter/smoother
dc.subjectKalman filter/smoother
dc.subjectLp convergence
dc.subjectLeast squares
dc.subjectLevenberg–Marquardt method
dc.titleOn the convergence of a non-linear ensemble Kalman smoother
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalApplied Numerical Mathematics
dc.eprint.versionPost-print
dc.contributor.institutionMaIAGE, INRA, Université Paris-Saclay, Jouy-en-Josas, 78350, , , , France
dc.contributor.institutionINP-ENSEEIHT and CERFACS, Toulouse, , , France
dc.contributor.institutionInstitute of Computer Science, Academy of Sciences of the Czech Republic, Prague, , , Czech Republic
dc.contributor.institutionUniversity of Colorado Denver, Denver, CO, , United States
dc.identifier.arxivid1411.4608
kaust.personBergou, El Houcine
refterms.dateFOA2018-12-23T08:12:21Z
dc.date.published-online2018-11-29
dc.date.published-print2019-03


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