Skip to Main content Skip to Navigation
Journal articles

A counter-example to the general convergence of partially greedy algorithms

Abstract : In a separable Hilbert space $\mathcalH$, greedy algorithms iteratively define $m$-term approximants to a given vector from a complete redundant dictionary $\Dict$. With very large dictionaries, the pure greedy algorithm cannot be implemented and must be replaced with a weak greedy algorithm. In numerical applications, \em partially greedy algorithms have been introduced to reduce the numerical complexity. A conjecture about their convergence arises naturally from the observation of numerical experiments. We introduce, study and disprove this conjecture.
Complete list of metadata
Contributor : Rémi Gribonval Connect in order to contact the contributor
Submitted on : Tuesday, March 15, 2011 - 9:39:43 AM
Last modification on : Wednesday, October 20, 2021 - 12:17:25 AM
Long-term archiving on: : Thursday, June 16, 2011 - 2:34:22 AM


Files produced by the author(s)



Rémi Gribonval. A counter-example to the general convergence of partially greedy algorithms. Journal of Approximation Theory, Elsevier, 2001, 111 (1), pp.128-138. ⟨10.1006/jath.2001.3556⟩. ⟨inria-00576644⟩



Record views


Files downloads