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Stationary Subdivision.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1991Copyright date: ©1991Edition: 1st edDescription: 1 online resource (197 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470408794
Subject(s): Genre/Form: Additional physical formats: Print version:: Stationary SubdivisionDDC classification:
  • 511/.42
LOC classification:
  • QA224 -- .C383 1991eb
Online resources:
Contents:
Intro -- 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.
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Intro -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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