Skip to Main content Skip to Navigation
Journal articles

A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method

Abstract : Using a preconditioned Richardson iterative method as a regularization to the data completion problem is the aim of the contribution. The problem is known to be exponentially ill posed that makes its numerical treatment a hard task. The approach we present relies on the Steklov-Poincaré variational framework introduced in [Inverse Problems, vol. 21, 2005]. The resulting algorithm turns out to be equivalent to the Kozlov-Maz’ya-Fomin method in [Comp. Math. Phys., vol. 31, 1991]. We conduct a comprehensive analysis on the suitable stopping rules that provides some optimal estimates under the General Source Condition on the exact solution. Some numerical examples are finally discussed to highlight the performances of the method.
Document type :
Journal articles
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download

https://hal.inria.fr/hal-01286821
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Friday, March 11, 2016 - 2:23:56 PM
Last modification on : Sunday, June 26, 2022 - 9:44:00 AM
Long-term archiving on: : Sunday, November 13, 2016 - 3:51:10 PM

File

Vol.13.pp.17-32.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Duc Thang Du, Faten Jelassi. A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2010, Volume 13 - 2010 - Special issue TAMTAM'09, pp.17-32. ⟨10.46298/arima.1934⟩. ⟨hal-01286821⟩

Share

Metrics

Record views

36

Files downloads

542