Comptes Rendus
no. 7
Probability Theory
Consistency of Landweber algorithm in an ill-posed problem with random data
[Consistance de l'algorithme de Landweber pour un problème mal posé avec des erreurs aléatoires]

Présenté par : Paul Deheuvels

Abdelnasser Dahmani1 ; Fatah Bouhmila1
1 Department of Mathematics, Laboratory of Applied Mathematics, University of Bejaia, 06000 Bejaia, Algeria
Comptes Rendus. Mathématique, Volume 343 (2006) no. 7, pp. 487-491.

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 l'existence et l'unicité de la pseudo-solution du problème puis nous l'estimons en utilisant l'algorithme de Landweber. Par ailleurs, nous montrons la convergence presque complète (p.co) de celui-ci tout en précisant la vitesse de convergence et nous construisons un domaine de confiance pour ladite pseudo-solution.

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’ (a.co) of this algorithm specifying its convergence rate. We finally build a confidence domain for the so mentioned pseudo-solution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.010

Abdelnasser Dahmani 1 ; Fatah Bouhmila 1

1 Department of Mathematics, Laboratory of Applied Mathematics, University of Bejaia, 06000 Bejaia, Algeria 
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Abdelnasser Dahmani; Fatah Bouhmila. Consistency of Landweber algorithm in an ill-posed problem with random data. Comptes Rendus. Mathématique, Volume 343 (2006) no. 7, pp. 487-491. doi : 10.1016/j.crma.2006.09.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.010/

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