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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2021 Volume 110, Issue 1, Pages 17–28 (Mi mzm13061)

This article is cited in 2 papers

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.

UDC: 517.518.8

Received: 01.03.2021

DOI: 10.4213/mzm13061


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

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© Steklov Math. Inst. of RAS, 2025