Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    5 0 0 0


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 

Abstract

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. 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.
Résumé

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 (p.co) 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.


© 2006  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@