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    On the convergence of a non-linear ensemble Kalman smoother

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    Type
    Article
    Authors
    Bergou, El Houcine
    Gratton, Serge
    Mandel, Jan
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-11-29
    Online Publication Date
    2018-11-29
    Print Publication Date
    2019-03
    Permanent link to this record
    http://hdl.handle.net/10754/630346
    
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    Abstract
    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 BV
    Journal
    Applied Numerical Mathematics
    DOI
    10.1016/j.apnum.2018.11.008
    arXiv
    1411.4608
    Additional Links
    https://www.sciencedirect.com/science/article/pii/S0168927418302575
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.apnum.2018.11.008
    Scopus Count
    Collections
    Articles; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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