On convergence rates of adaptive ensemble Kalman inversion for linear ill-posed problems.
47A52
65C05
65J20
Journal
Numerische mathematik
ISSN: 0029-599X
Titre abrégé: Numer Math (Heidelb)
Pays: Germany
ID NLM: 101705647
Informations de publication
Date de publication:
2022
2022
Historique:
received:
20
04
2021
revised:
21
02
2022
accepted:
15
06
2022
entrez:
30
9
2022
pubmed:
1
10
2022
medline:
1
10
2022
Statut:
ppublish
Résumé
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able to introduce a new sampling scheme based on the Nyström method that improves practical performance. Furthermore, we formulate an adaptive version of ensemble Kalman inversion where the sample size is coupled with the regularization parameter. We prove that the proposed scheme yields an order optimal regularization method under standard assumptions if the discrepancy principle is used as a stopping criterion. The paper concludes with a numerical comparison of the discussed methods for an inverse problem of the Radon transform.
Identifiants
pubmed: 36176672
doi: 10.1007/s00211-022-01314-y
pii: 1314
pmc: PMC9510123
doi:
Types de publication
Journal Article
Langues
eng
Pagination
371-409Informations de copyright
© The Author(s) 2022.
Références
PeerJ. 2014 Jun 19;2:e453
pubmed: 25024921
Numer Funct Anal Optim. 2016 Feb 2;37(5):521-540
pubmed: 27499565
Nat Methods. 2020 Mar;17(3):261-272
pubmed: 32015543
Nature. 2020 Sep;585(7825):357-362
pubmed: 32939066