%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 %~ UNIV-PARIS7 %~ UPMC %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INSMI %~ LJLL %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2 %~ TDS-MACS %~ UPMC_POLE_1 %~ SORBONNE-UNIVERSITE %~ SU-SCIENCES %~ UNIV-PARIS %~ ALLIANCE-SU