Mathematical Notes

, Volume 78, Issue 1–2, pp 170–184 | Cite as

Generalized Approximate Weak Greedy Algorithms

  • V. V. Galatenko
  • E. D. Livshits


We study generalized approximate weak greedy algorithms. The main difference of these algorithms from approximate weak greedy algorithms proposed by R. Gribonval and M. Nielsen consists in that errors in the calculation of the coefficients can be prescribed in terms of not only their relative values, but also their absolute values. We present conditions on the parameters of generalized approximate weak greedy algorithms which are sufficient for the expansions resulting from the use of this algorithm to converge to the expanded element. It is shown that these conditions cannot be essentially weakened. We also study some questions of the convergence of generalized approximate weak greedy expansions with respect to orthonormal systems.

Key words

generalized approximate weak greedy algorithm pure greedy algorithm matching pursuit Hilbert space orthonormal system 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. V. Galatenko
    • 1
  • E. D. Livshits
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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