Título original |
Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies. |
Título inglés |
Study of the rate of convergence of the cascade algorithm in the construction of Ingrid Daubechies's wavelets. |
Título español |
Estudio de la velocidad de convergencia del algoritmo en cascada en la construcción de ondículas de Ingrid Daubechies. |
Autor/es |
Durand, Sylvie |
Organización |
CEREMADE Univ. París IX-Dauphine, París, Francia |
Revista |
0213-2230 |
Publicación |
1996, 12 (2): 227-297, 17 Ref. |
Tipo de documento |
articulo |
Idioma |
Francés |
Resumen inglés |
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. |
Clasificación UNESCO |
120607 |
Palabras clave español |
Ondículas ; Algoritmos numéricos ; Funciones de escala ; Ajuste de curvas ; Ajuste de superficies ; Interpolación ; Métodos iterativos |
Código MathReviews |
MR1402669 |
Código Z-Math |
Zbl 0865.65103 |
Acceso al artículo completo |