Numerical Algorithms

, Volume 4, Issue 3, pp 307–322

Convergence of cascade algorithms introduced by I. Daubechies

  • Sylvain Durand
Article

Abstract

Orthonormal wavelets are often constructed by an iteration procedure commonly referred to as thecascade algorithm. We obtain an asymptotic expansion and deduce necessary and sufficient conditions for convergence in Sobolev norms.

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References

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    I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988).Google Scholar
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    P.G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana (1986) 1–18.Google Scholar
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    Y. Meyer,Ondelettes et Opérateurs (Hermann, 1990).Google Scholar
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    Y. Meyer and F. Paiva, Remarques sur la construction des ondelettes orthogonales, to be published.Google Scholar
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    P. Verlinden and A. Haegemans, An asymptotic expansion in wavelet analysis and its application to accurate numerical wavelet decomposition, Numer. Algor. 2 (1992) 287–298.Google Scholar
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    L.F. Villemoes, Wavelet analysis of two-scale difference equations, to be published.Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Sylvain Durand
    • 1
  1. 1.CEREMADEUniversité Paris-DauphineParis Cedex 16France

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