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.
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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, Volume 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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