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Comptes Rendus Mathématique
Volume 347, n° 23-24
pages 1435-1438 (décembre 2009)
Doi : 10.1016/j.crma.2009.09.026
Received : 24 April 2008 ;  accepted : 30 September 2009
A proximal approach to the inversion of ill-conditioned matrices
Une approche proximale de l’inversion des matrices mal-conditionnées
 

Pierre Maréchal a , Aude Rondepierre b
a Institut de mathématiques, université Paul-Sabatier, 31062 Toulouse cedex 9, France 
b Institut de mathématiques, INSA de Toulouse, département GMM, 31077 Toulouse cedex 4, France 

Abstract

We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization parameter ) belongs to the class of fixed point methods. Convergence of the algorithm is also discussed. To cite this article: P. Maréchal, A. Rondepierre, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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

Nous proposons un algorithme proximal général pour l’inversion de matrices mal-conditionnées. Cet algorithme est basé sur une caractérisation variationnelle des pseudo-inverses. Nous montrons qu’un cas particulier (avec paramètre de régularisation constant) appartient à la classe des méthodes de point fixe . La convergence de l’algorithme est aussi considérée et discutée. Pour citer cet article : P. Maréchal, A. Rondepierre, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

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


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