# 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.
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https://hal.inria.fr/inria-00576644
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Submitted on : Tuesday, March 15, 2011 - 9:39:43 AM
Last modification on : Wednesday, October 20, 2021 - 12:17:25 AM
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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⟩

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