| Issue |
RAIRO-Oper. Res.
Volume 47, Number 3, July-September 2013
|
|
|---|---|---|
| Page(s) | 299 - 310 | |
| DOI | https://doi.org/10.1051/ro/2013040 | |
| Published online | 26 August 2013 | |
From Eckart and Young approximation to Moreau envelopes and vice versa
Institute of Mathematics, Paul Sabatier University, 118 Route de Narbonne,
31400 Toulouse, France. ; http://www.math.univ-toulouse.fr/˜jbhu/
jbhu@math.univ-toulouse.fr; hyle@math.univ-toulouse.fr
Received:
6
June
2013
Accepted:
21
June
2013
In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.
Mathematics Subject Classification: 15A / 46N10 / 65K10 / 90C
Key words: Eckart and Young theorem / moreau envelopes / rank minimization problems
© EDP Sciences, ROADEF, SMAI, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.