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Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli
| Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli |
| Autore | Cavaretta Alfred S. <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
| Descrizione fisica | 1 online resource (197 p.) |
| Disciplina | 511/.42 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Spline theory
Algorithms Computer graphics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0879-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 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 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 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"" |
| Record Nr. | UNINA-9910480572403321 |
Cavaretta Alfred S. <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli
| Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli |
| Autore | Cavaretta Alfred S. <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
| Descrizione fisica | 1 online resource (197 p.) |
| Disciplina | 511/.42 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Spline theory
Algorithms Computer graphics |
| ISBN | 1-4704-0879-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 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 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 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"" |
| Record Nr. | UNINA-9910788876503321 |
|
Cavaretta Alfred S. <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli
| Stationary subdivision / / Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli |
| Autore | Cavaretta Alfred S. <1944-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1991 |
| Descrizione fisica | 1 online resource (197 p.) |
| Disciplina | 511/.42 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Spline theory
Algorithms Computer graphics |
| ISBN | 1-4704-0879-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 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 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 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"" |
| Record Nr. | UNINA-9910827869403321 |
|
Cavaretta Alfred S. <1944->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1991 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||