A stochastic procedure to solve linear ill-posed problems |
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Authors: | Fouad Maouche Abdelnasser Dahmani Nadji Rahmania |
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Institution: | 1. Laboratoire de Mathématiques Appliquées, Faculté des Sciences Exactes, Université de Bejaia, Bejaia, Algérie;2. Laboratoire Paul Painlevé, USTL-UMR-CNRS 8524.UFR de Mathématiques, Villeneuve d’Ascq Cédex, France |
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Abstract: | In this work, we propose a stochastic procedure of Robbins–Monro type to resolve linear inverse problems in Hilbert space. We study the probability of large deviation between the exact solution and the approximated one and build a confidence domain for the approximated solution while precising the rate of convergence. To check the validity of our work, we give a simulation application into a deconvolution problem. |
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Keywords: | Deconvolution ill-posed problem inverse problem Robbins-Monro |
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