Volume 47, Number 3, July-September 2013
|Page(s)||299 - 310|
|Published online||26 August 2013|
From Eckart and Young approximation to Moreau envelopes and vice versa
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
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