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Projection Greedy Algorithm

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Abstract

We introduce and study a new type of greedy algorithm, namely, projection greedy algorithms with respect to a given dictionary in a Hilbert space. We prove that these algorithms converge and estimate the rate of convergence for initial elements from the convex hull of the dictionary. Several specific examples of dictionaries are used to compare the introduced algorithms with orthogonal greedy algorithms.

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References

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    P. A. Borodin & S. V. Konyagin

  2. Moscow Center of Fundamental and Applied Mathematics, Moscow, 119991, Russia

    P. A. Borodin

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991, Russia

    S. V. Konyagin

Authors
  1. P. A. Borodin
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  2. S. V. Konyagin
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Corresponding author

Correspondence to P. A. Borodin.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 17-28 https://doi.org/10.4213/mzm13061.

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Borodin, P.A., Konyagin, S.V. Projection Greedy Algorithm. Math Notes 110, 16–25 (2021). https://doi.org/10.1134/S0001434621070026

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  • DOI: https://doi.org/10.1134/S0001434621070026

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