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Stationary subdivision /
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
1991.
|
| Colección: | Memoirs of the American Mathematical Society ;
Volume 93, no. 453. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Table of Contents
- 1. Introduction
- 2. Subdivision Schemes: Convergence Concepts and the Associated Functional Equation
- 2.1. The form of the limiting surface of uniformly convergent subdivision schemes
- 2.2. Consequences of the finite support of the mask
- 2.3. Other notions of convergence; weakly convergent schemes
- 2.4. Matrix masks
- 3. Contractivity of the Subdivision Operator
- 3.1. Contractivity as a convergence criterion
- 3.2. Contractivity for masks supported on convex sets
- 3.3. Contractivity via factorization of the subdivision operator
- ""4. Subdivision from Dimension Compression""""4.1. Compression of the refinable function[omitted]""; ""4.2. The algebra of compressed schemes""; ""4.3. Convergence theorems for compressed schemes""; ""4.4. The line average algorithm""; ""5. Solution of the Functional Equation""; ""5.1. Necessary conditions in terms of the geometric mean""; ""5.2. Sufficient conditions based on the Paley�Wiener theorem""; ""5.3. Conditions for convergence of the subdivision scheme suggested by the mean ergodic theorem""; ""6. Algebraic Properties of Subdivision Schemes""
- 6.1. The subdivision operator on polynomial sequences6.2. Spectral properties of S on polynomial sequence spaces
- 6.3. Polynomial subspaces generated by convergent subdivision schemes
- 6.4. Matrix representation for a local convergence analysis of regular subdivision schemes; matrix subdivision schemes
- 7. Matrix Refinement Equation
- 7.1. Contractivity for matrix subdivision schemes
- 7.2. Definition of refinement pairs
- 7.3. Refinement pairs which produce polynomial surfaces
- ""7.4. Necessary and sufficient conditions for the generation of smooth surfaces by a refinement pair""""7.5. The fractal nature of surfaces generated by a refinement pair""; ""8. Smoothness of S�Refinable Functions and Consequences""; ""8.1. Determining smoothness of the refinahle function using differenced subdivision schemes""; ""8.2. Subdivision schemes with smooth refinahle functions generate polynomials""; ""8.3. Univariate subdivision schemes producing piecewise polynomial functions""; ""9. Appendix""; ""References""