A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data

Laurent Bourgeois 1 Jérémi Dardé 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, we introduce a new version of the method of quasi-reversibility to solve the ill-posed Cauchy problems for the Laplace's equation in the presence of noisy data. It enables one to regularize the noisy Cauchy data and to select a relevant value of the regularization parameter in order to use the standard method of quasi-reversibility. Our method is based on duality in optimization and is inspired by the Morozov's discrepancy principle. Its efficiency is shown with the help of some numerical experiments in two dimensions. © 2010 IOP Publishing Ltd.
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Laurent Bourgeois, Jérémi Dardé. A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data. Inverse Problems, IOP Publishing, 2010, 26 (9), pp.095016. ⟨10.1088/0266-5611/26/9/095016⟩. ⟨hal-00873058⟩

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