Comptes Rendus
no. 23-24
Numerical Analysis
A proximal approach to the inversion of ill-conditioned matrices

Presented by: Philippe G. Ciarlet

Pierre Maréchal1; Aude Rondepierre2
1 Institut de mathématiques, université Paul-Sabatier, 31062 Toulouse cedex 9, France
2 Institut de mathématiques, INSA de Toulouse, département GMM, 31077 Toulouse cedex 4, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1435-1438.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.09.026

Pierre Maréchal 1; Aude Rondepierre 2

1 Institut de mathématiques, université Paul-Sabatier, 31062 Toulouse cedex 9, France
2 Institut de mathématiques, INSA de Toulouse, département GMM, 31077 Toulouse cedex 4, France 
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Pierre Maréchal; Aude Rondepierre. A proximal approach to the inversion of ill-conditioned matrices. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1435-1438. doi : 10.1016/j.crma.2009.09.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.026/

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