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Some remarks on greedy algorithms

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Abstract

Estimates are given for the rate of approximation of a function by means of greedy algorithms. The estimates apply to approximation from an arbitrary dictionary of functions. Three greedy algorithms are discussed: the Pure Greedy Algorithm, an Orthogonal Greedy Algorithm, and a Relaxed Greedy Algorithm.

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References

  1. A. Barron, Universal approximation bounds for superposition of a sigmoidal function, IEEE Transactions on Information Theory 39 (1993) 930–945.

    Article  Google Scholar 

  2. C. Darken, M. Donahue, L. Gurvits and E. Sontag, Rate of approximation results motivated by robust neural network learning,6th ACM Conference on Computer Learning Theory, ACM, 1993, pp. 303–309.

  3. R. DeVore, B. Jawerth and V. Popov, Compression of wavelet decompositions, American Journal of Mathematics 114 (1992) 737–785.

    Google Scholar 

  4. L. Jones, A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training, Annals of Statistics 20 (1992) 608–613.

    Google Scholar 

  5. G. Davis, S. Mallat and M. Avellaneda, Adaptive nonlinear approximations, Constructure Approximation, to appear.

  6. E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen. I, Math. Annalen 63 (1906–1907) 433–476.

    Article  Google Scholar 

  7. S.B. Stechkin, On absolute convergence of orthogonal series, Dok. Akad. Nauk SSSR 102 (1955) 37–40.

    Google Scholar 

  8. G. Pisier, Remarques sur un resultat non publié de B. Maurey,Seminaire d'Analyse Fonctionelle, 1980–81, Ecole Polytechnique Centre de Mathematiques, Palaiseau.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, 29208, Columbia, SC, USA

    R. A. DeVore & V. N. Temlyakov

Authors
  1. R. A. DeVore
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  2. V. N. Temlyakov
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Additional information

This research was supported by the Office of Naval Research Contract N0014-91-J1343.

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DeVore, R.A., Temlyakov, V.N. Some remarks on greedy algorithms. Adv Comput Math 5, 173–187 (1996). https://doi.org/10.1007/BF02124742

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  • DOI: https://doi.org/10.1007/BF02124742

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