Convergence analysis of ensemble Kalman inversion: the linear, noisy case. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Schillings, C.; Stuart, A. M.
• Is Part Of: Applicable analysis. Volume 97:Issue 1(2018)
• Page Start: 107
• Page End: 123
• Publication Date: 2018-01-02
• Subjects: Bayesian inverse problems -- ensemble Kalman filter -- parameter identification; 65N21 -- 62F15 -- 65N75; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1386784
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: 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.