[Une approche proximale de l'inversion des matrices mal-conditionnées]
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.
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.
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@article{CRMATH_2009__347_23-24_1435_0,
author = {Mar\'echal, Pierre and Rondepierre, Aude},
title = {A proximal approach to the inversion of ill-conditioned matrices},
journal = {Comptes Rendus. Math\'ematique},
pages = {1435--1438},
publisher = {Elsevier},
volume = {347},
number = {23-24},
year = {2009},
doi = {10.1016/j.crma.2009.09.026},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.09.026/}
}
TY - JOUR AU - Maréchal, Pierre AU - Rondepierre, Aude TI - A proximal approach to the inversion of ill-conditioned matrices JO - Comptes Rendus. Mathématique PY - 2009 SP - 1435 EP - 1438 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.09.026/ DO - 10.1016/j.crma.2009.09.026 LA - en ID - CRMATH_2009__347_23-24_1435_0 ER -
%0 Journal Article %A Maréchal, Pierre %A Rondepierre, Aude %T A proximal approach to the inversion of ill-conditioned matrices %J Comptes Rendus. Mathématique %D 2009 %P 1435-1438 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.09.026/ %R 10.1016/j.crma.2009.09.026 %G en %F CRMATH_2009__347_23-24_1435_0
Maréchal, Pierre; Rondepierre, Aude. A proximal approach to the inversion of ill-conditioned matrices. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1435-1438. doi : 10.1016/j.crma.2009.09.026. http://www.numdam.org/articles/10.1016/j.crma.2009.09.026/
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