Study of the rate of convergence of the cascade algorithm in the construction of Ingrid Daubechies's wavelets.

Sylvie Durand

Revista Matemática Iberoamericana (1996)

  • Volume: 12, Issue: 2, page 227-297
  • ISSN: 0213-2230

Abstract

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The aim of this paper is the study of the convergence of algorithms involved in the resolution of two scale equations. They are fixed point algorithms, often called cascade algorithms, which are used in the construction of wavelets. We study their speed of convergence in Lebesgue and Besov spaces, and show that the quality of the convergence depends on two independent factors. The first one, as we could foresee, is the regularity of the scaling function which is the solution of the equation. The second factor (that is the essential discovery of this work) concerns specific algebraic properties of the function used to initialize the algorithm. This function must satisfy conditions analogous to Strang-Fix conditions.

How to cite

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Durand, Sylvie. "Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.." Revista Matemática Iberoamericana 12.2 (1996): 227-297. <http://eudml.org/doc/39508>.

@article{Durand1996,
author = {Durand, Sylvie},
journal = {Revista Matemática Iberoamericana},
keywords = {Ondículas; Algoritmos numéricos; Funciones de escala; Ajuste de curvas; Ajuste de superficies; Interpolación; Métodos iterativos; convergence; cascade algorithm; wavelets},
language = {fre},
number = {2},
pages = {227-297},
title = {Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.},
url = {http://eudml.org/doc/39508},
volume = {12},
year = {1996},
}

TY - JOUR
AU - Durand, Sylvie
TI - Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.
JO - Revista Matemática Iberoamericana
PY - 1996
VL - 12
IS - 2
SP - 227
EP - 297
LA - fre
KW - Ondículas; Algoritmos numéricos; Funciones de escala; Ajuste de curvas; Ajuste de superficies; Interpolación; Métodos iterativos; convergence; cascade algorithm; wavelets
UR - http://eudml.org/doc/39508
ER -

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