KAUST DepartmentVisual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2018-11-29
Print Publication Date2019-03
Permanent link to this recordhttp://hdl.handle.net/10754/630346
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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.
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.
SponsorsPartially 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.
JournalApplied Numerical Mathematics