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A proximal approach to the inversion of ill-conditioned matrices

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 {\sl fixed point} methods. Convergence of the algorithm is also discussed.
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https://hal.archives-ouvertes.fr/hal-00373356
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Submitted on : Saturday, April 4, 2009 - 12:56:26 PM
Last modification on : Friday, November 26, 2021 - 6:20:32 PM
Long-term archiving on: : Thursday, June 10, 2010 - 7:46:21 PM

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  • HAL Id : hal-00373356, version 1
  • ARXIV : 0904.0703

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

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