%0 Journal Article
%T A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%+ Laboratoire Jacques-Louis Lions (LJLL)
%A Bourgeois, Laurent
%A Dardé, Jérémi
%< avec comité de lecture
%@ 0266-5611
%J Inverse Problems
%I IOP Publishing
%V 26
%N 9
%P 095016
%8 2010
%D 2010
%R 10.1088/0266-5611/26/9/095016
%Z Mathematics [math]/Numerical Analysis [math.NA]Journal articles
%X 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.
%G English
%L hal-00873058
%U https://hal-ensta-paris.archives-ouvertes.fr/hal-00873058
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%~ INRIA2
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%~ SORBONNE-UNIVERSITE
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