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

Laurent Bourgeois; Jérémi Dardé

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

2 LJLL - Laboratoire Jacques-Louis Lions

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.

Document type :

Journal articles

Domain :

Mathematics [math] / Numerical Analysis [math.NA]

Complete list of metadatas

https://hal-ensta-paris.archives-ouvertes.fr//hal-00873058
Contributor : Aurélien Arnoux <>
Submitted on : Tuesday, October 15, 2013 - 12:03:18 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:03 AM

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

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

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