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Mat. Zametki, 2021, Volume 110, Issue 1, Pages 17–28 (Mi mz13061)  

Projection Greedy Algorithm

P. A. Borodinab*, S. V. Konyaginac

a Laboratory "Multidimensional Approximation and Applications", Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We introduce and study a new type of greedy algorithms, namely, the projection greedy algorithm with respect to a given dictionary in a Hilbert space. We prove its convergence 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 algorithm with the orthogonal greedy algorithm.

Keywords: greedy approximations, Hilbert space, rate of convergence.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
This work was supported by the Grant of the Government of the Russian Federation (grant no. 14.W03.31.0031).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm13061

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English version:
Mathematical Notes, 2021, 110:1, 16–25

Bibliographic databases:

UDC: 517.518.8
Received: 01.03.2021

Citation: P. A. Borodin, S. V. Konyagin, “Projection Greedy Algorithm”, Mat. Zametki, 110:1 (2021), 17–28; Math. Notes, 110:1 (2021), 16–25

Citation in format AMSBIB
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\by P.~A.~Borodin, S.~V.~Konyagin
\paper Projection Greedy Algorithm
\jour Mat. Zametki
\yr 2021
\vol 110
\issue 1
\pages 17--28
\mathnet{http://mi.mathnet.ru/mz13061}
\crossref{https://doi.org/10.4213/mzm13061}
\transl
\jour Math. Notes
\yr 2021
\vol 110
\issue 1
\pages 16--25
\crossref{https://doi.org/10.1134/S0001434621070026}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000687705200002}


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  • https://doi.org/10.4213/mzm13061
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