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Mathematical Notes

, Volume 92, Issue 3–4, pp 485–489 | Cite as

Comparison of the convergence rate of pure greedy and orthogonal greedy algorithms

  • A. V. DereventsovEmail author
Article
  • 362 Downloads

Abstract

The following two types of greedy algorithms are considered: the pure greedy algorithm (PGA) and the orthogonal greedy algorithm (OGA). From the standpoint of estimating the rate of convergence on the entire class A 1(D), the orthogonal greedy algorithm is optimal and significantly exceeds the pure greedy algorithm. The main result in the present paper is the assertion that the situation can also be opposite for separate elements of the class A 1(D) (and even of the class A 0(D)): the rate of convergence of the orthogonal greedy algorithm can be significantly lower than the rate of convergence of the pure greedy algorithm.

Keywords

pure greedy algorithm orthogonal greedy algorithm dictionary rate of convergence Hilbert space the classes A1(D) and A0(D

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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