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Mat. Zametki, 2005, Volume 78, Issue 2, Pages 186–201 (Mi mz2581)  

This article is cited in 10 scientific papers (total in 10 papers)

Generalized Approximate Weak Greedy Algorithms

V. V. Galatenkoa, E. D. Livshitsb

a M. V. Lomonosov Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/mzm2581

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English version:
Mathematical Notes, 2005, 78:2, 170–184

Bibliographic databases:

UDC: 517.518+517.988+519.651
Received: 08.04.2004

Citation: V. V. Galatenko, E. D. Livshits, “Generalized Approximate Weak Greedy Algorithms”, Mat. Zametki, 78:2 (2005), 186–201; Math. Notes, 78:2 (2005), 170–184

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. D. Livshits, “On $n$-Term Approximation with Positive Coefficients”, Math. Notes, 82:3 (2007), 332–340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. D. Livshits, “Lower bounds for the rate of convergence of greedy algorithms”, Izv. Math., 73:6 (2009), 1197–1215  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. A. V. Dereventsov, “Comparison of the Convergence Rate of Pure Greedy and Orthogonal Greedy Algorithms”, Math. Notes, 92:4 (2012), 485–489  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. Yu. Kudryavtsev, “On the Convergence of Orthorecursive Expansions in Nonorthogonal Wavelets”, Math. Notes, 92:5 (2012), 643–656  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Tian W., Rui G., “Blind Sparsity Weak Subspace Pursuit for Compressed Sensing”, Electron. Lett., 49:5 (2013), 369–U86  crossref  isi  elib  scopus  scopus
    6. N. N. Fedotov, “Convergence of orthogonal greedy algorithm with errors in projectors”, Moscow University Mathematics Bulletin, 68:1 (2013), 37–41  mathnet  crossref  mathscinet
    7. Galatenko V.V., Lebedev A.E., Nechaev I.N., Shkurnikov M.Yu., Tonevitskii E.A., Podol'skii V.E., “On the Construction of Medical Test Systems Using Greedy Algorithm and Support Vector Machine”, Bull. Exp. Biol. Med., 156:5 (2014), 706–709  crossref  isi  scopus  scopus
    8. Dereventsov A., “On the Generalized Approximate Weak Chebyshev Greedy Algorithm”, Studia Math., 237:2 (2017), 153–175  crossref  mathscinet  zmath  isi  scopus
    9. Dereventsov V A., Temlyakov V.N., “A Unified Way of Analyzing Some Greedy Algorithms”, J. Funct. Anal., 277:12 (2019), UNSP 108286  crossref  mathscinet  isi
    10. Al. R. Valiullin, Ar. R. Valiullin, V. V. Galatenko, “Freimy kak nepreryvnye izbytochnye kody”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2021, no. 2, 39–43  mathnet
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