A proximal approach to the inversion of ill-conditioned matrices

Pierre Maréchal (1) , Aude Rondepierre (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 {\sl fixed point} methods. Convergence of the algorithm is also discussed.

Mots clés: Algorithme proximal; pseudo-inverse.

Mots clés: pseudo-inverse

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Pierre Maréchal, Aude Rondepierre. A proximal approach to the inversion of ill-conditioned matrices. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347 (23-24), pp.Pages 1435-1438. ⟨hal-00373356⟩