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Approximate Weak Greedy Algorithms

Abstract : We present a generalization of V. Temlyakov's weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a class of dictionaries with more structure, we give a more relaxed necessary and sufficient condition for convergence of the algorithm. We also provide as detailed discussion of how a "real-world" implementation of the weak greedy algorithm, when one has to take into account floating point arithmetic and other types of finite precision errors, can be modeled by the new algorithm.
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https://hal.inria.fr/inria-00576643
Contributor : Rémi Gribonval <>
Submitted on : Tuesday, March 15, 2011 - 9:32:33 AM
Last modification on : Thursday, August 22, 2019 - 2:02:39 PM
Long-term archiving on: : Thursday, June 16, 2011 - 2:33:44 AM

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Rémi Gribonval, Morten Nielsen. Approximate Weak Greedy Algorithms. Advances in Computational Mathematics, Springer Verlag, 2001, 14 (4), pp.361-378. ⟨10.1023/A:1012255021470⟩. ⟨inria-00576643⟩

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