04084nam 2200625 450 991048057240332120170821172539.01-4704-0879-1(CKB)3360000000464637(EBL)3113883(SSID)ssj0000889232(PQKBManifestationID)11521352(PQKBTitleCode)TC0000889232(PQKBWorkID)10875648(PQKB)10775682(MiAaPQ)EBC3113883(PPN)195413369(EXLCZ)99336000000046463720140908h19911991 uy 0engur|n|---|||||txtccrStationary subdivision /Alfred S. Cavaretta, Wolfgang Dahmen, Charles A. MicchelliProvidence, Rhode Island :American Mathematical Society,1991.©19911 online resource (197 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 93, Number 453"September 1991, Volume 93, Number 453 (second of 3 numbers)."0-8218-2507-0 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 93, Number 453.Spline theoryAlgorithmsComputer graphicsElectronic books.Spline theory.Algorithms.Computer graphics.511/.42Cavaretta Alfred S.1944-903058Dahmen Wolfgang1949-Micchelli Charles A.MiAaPQMiAaPQMiAaPQBOOK9910480572403321Stationary subdivision2018742UNINA