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Comptes Rendus Mathématique
Volume 343, n° 7
pages 487-491 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.010
Received : 7 February 2006 ;  accepted : 5 September 2006
Consistency of Landweber algorithm in an ill-posed problem with random data
Consistance de lʼalgorithme de Landweber pour un problème mal posé avec des erreurs aléatoires

Abdelnasser Dahmani , Fatah Bouhmila
Department of Mathematics, Laboratory of Applied Mathematics, University of Bejaia, 06000 Bejaia, Algeria 


This Note deals with the linear ill-posed problem, described by operator equations in which the second member is measured with random errors. We first show the existence and the unicity of the pseudo-solution for such a problem and later estimate it using Landweber algorithm. We also show the almost complete convergence' ( of this algorithm specifying its convergence rate. We finally build a confidence domain for the so mentioned pseudo-solution. To cite this article: A. Dahmani, F. Bouhmila, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.

Dans cette Note, nous considérons un problème mal posé linéaire décrit par une équation à opérateur où le second membre est mesuré avec des erreurs aléatoires. Nous montrons lʼexistence et lʼunicité de la pseudo-solution du problème puis nous lʼestimons en utilisant lʼalgorithme de Landweber. Par ailleurs, nous montrons la convergence presque complète ( de celui-ci tout en précisant la vitesse de convergence et nous construisons un domaine de confiance pour ladite pseudo-solution. Pour citer cet article : A. Dahmani, F. Bouhmila, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.

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