Analyse hilbertienne pour le traitement des données

  • Voir la page en français

    In brief

  • Code : N8EN05A

Objectives

Hilbert spaces are instrumental for solving problems whose unknown is a function. They are used for solving PDE’s when the spectral method is concerned. They provide also a powerful framework for Fourier and Wavelet decomposition. Finally separations results are essential for many convex machine-learning algorithms. The goal of the course is to provide a rigorous exposition of these concepts, and to illustrate them on practical examples from PDE’s and signal processing.

In a second part, we are interested in the numerical resolution of optimal control problems with ordinary differential equations. Such problems arise in many applications: orbital transfer, medical imaging… The goal is to solve efficiently the large scale optimization problem obtained via the discretization of the optimal control problem.

Bibliography

Une exploration des signaux en ondelettes, S. Mallat, Les Editions de l’Ecole Polytechnique, 2000
Analyse réelle et complexe : Cours et exercices, W. Rudin
Dérivation, intégration, édition revue et augmentée, C. Wagschal, Hermann éditeurs, 2012
Analyse numérique et équations différentielles, J.-P. Demailly, Presses Universitaires de Grenoble, 1996
Contrôle optimal : théorie & applications, E. Trélat, Vuibert, Collection "Ma- thématiques Concrètes", 2005

Session 1 ou session unique - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CT (contrôle terminal) Oral/Ecrit70%Examen Analyse Hibertienne
CT (contrôle terminal) Rapport30%Rapport Analyse Hibertienne

Session 2 - Contrôle des connaissances

ModalitéNatureCoefficientRemarques
CT (contrôle terminal) Oral/Ecrit70%Examen Analyse Hibertienne
CT (contrôle terminal) Rapport30%Rapport Analyse Hibertienne

Contact(s)

GRATTON SERGE

Places

  • Toulouse

Contact

The National Institute of Electrical engineering, Electronics, Computer science,Fluid mechanics & Telecommunications and Networks

2, rue Charles Camichel - BP 7122
31071 Toulouse Cedex 7, France

+33 (0)5 34 32 20 00

Certifications

  • Logo MENESR
  • Logo UTFTMP
  • Logo INP
  • Logo INPT
  • Logo Mines télécoms
  • Logo CTI
  • Logo CDEFI
  • Logo midisup