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Analytic approximation with real constraints, with applications to inverse diffusion problems

Juliette Leblond 1 Jean-Paul Marmorat 2 Jonathan R. Partington 3
1 APICS - Analysis and Problems of Inverse type in Control and Signal processing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 CMA - Centre de Mathématiques Appliquées
3 School of Mathematics - University of Leeds
Abstract : The methods of constrained approximation in Hilbert spaces of analytic functions are applied to the solution of the inverse problems of detecting cracks or sources in a two-dimensional material by means of boundary measurements. Issues of well-posedness are discussed, and results on continuity and robustness with respect to the given data are established. Constructive and efficient methods for resolution of the above approximation problems are presented. The techniques are illustrated by numerical examples incorporating a further rational approximation step.
Keywords : Approximation extremal problems analytic functions Hardy spaces Toeplitz and Hankel operators inverse problems
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Journal articles
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Submitted on : Tuesday, July 20, 2010 - 5:26:04 PM
Last modification on : Monday, November 23, 2020 - 2:46:25 PM

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Juliette Leblond, Jean-Paul Marmorat, Jonathan R. Partington. Analytic approximation with real constraints, with applications to inverse diffusion problems. Journal of Inverse and Ill-posed Problems, De Gruyter, 2008, 16 (1), pp.89-105. ⟨10.1515/JIIP.2008.007⟩. ⟨hal-00504626⟩

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