Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli

• Record Nr.: UNINA9910480572403321
• Autore: Cavaretta Alfred S. <1944->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1991; ©1991
• ISBN: 1-4704-0879-1
• Descrizione fisica: 1 online resource (197 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 93, Number 453
• Disciplina: 511/.42
• Soggetti: Spline theory; Algorithms; Computer graphics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "September 1991, Volume 93, Number 453 (second of 3 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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 Paleyâ€?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 sequences""""6.2. 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 Sâ€?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""