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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.
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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, 13, pp.17-32. ⟨hal-01286821⟩

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