Convergence analysis of ensemble Kalman inversion: the linear, noisy case

We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. We will build on recent results on the convergenc...

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Bibliographic Details
Published inApplicable analysis Vol. 97; no. 1; pp. 107 - 123
Main Authors Schillings, C., Stuart, A. M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2018
Taylor & Francis Ltd
Subjects
65N21
Bayesian inverse problems
Continuity (mathematics)
Convergence
ensemble Kalman filter
Inverse problems
Kalman filters
parameter identification
Well posed problems
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2017.1386784

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Summary:We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. We will build on recent results on the convergence in the noise-free case and generalise them to the case of noisy observational data, in particular the influence of the noise on the convergence will be investigated, both theoretically and numerically. We focus on linear inverse problems where a very complete theoretical analysis is possible.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2017.1386784