Type
ArticleKAUST Department
Visual Computing Center (VCC)Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2018-11-29Online Publication Date
2018-11-29Print Publication Date
2019-03Permanent link to this record
http://hdl.handle.net/10754/630346
Metadata
Show full item recordAbstract
Ensemble 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.Citation
Bergou 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.Sponsors
Partially 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.Publisher
Elsevier BVJournal
Applied Numerical MathematicsarXiv
1411.4608Additional Links
https://www.sciencedirect.com/science/article/pii/S0168927418302575ae974a485f413a2113503eed53cd6c53
10.1016/j.apnum.2018.11.008