Duc Thang Du ; Faten Jelassi - A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method

arima:1934 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, August 1, 2010, Volume 13 - 2010 - Special issue TAMTAM'09 - https://doi.org/10.46298/arima.1934
A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method

Authors: Duc Thang Du ; Faten Jelassi

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.


Volume: Volume 13 - 2010 - Special issue TAMTAM'09
Published on: August 1, 2010
Submitted on: January 6, 2010
Keywords: Cauchy problem, Regularization, iterative method, Morozov’s discrepancy principle.,Problème de Cauchy,Régularisation,Méthode itérative,Principe de Morozov,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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