LEADER 04084nam 2200625 450 001 9910480572403321 005 20170821172539.0 010 $a1-4704-0879-1 035 $a(CKB)3360000000464637 035 $a(EBL)3113883 035 $a(SSID)ssj0000889232 035 $a(PQKBManifestationID)11521352 035 $a(PQKBTitleCode)TC0000889232 035 $a(PQKBWorkID)10875648 035 $a(PQKB)10775682 035 $a(MiAaPQ)EBC3113883 035 $a(PPN)195413369 035 $a(EXLCZ)993360000000464637 100 $a20140908h19911991 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStationary subdivision /$fAlfred S. Cavaretta, Wolfgang Dahmen, Charles A. Micchelli 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1991. 210 4$dİ1991 215 $a1 online resource (197 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 93, Number 453 300 $a"September 1991, Volume 93, Number 453 (second of 3 numbers)." 311 $a0-8218-2507-0 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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 Paleya???Wiener theorem""; ""5.3. Conditions for convergence of the subdivision scheme suggested by the mean ergodic theorem""; ""6. Algebraic Properties of Subdivision Schemes"" 327 $a""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"" 327 $a""7.4. Necessary and sufficient conditions for the generation of smooth surfaces by a refinement pair""""7.5. The fractal nature of surfaces generated by a refinement pair""; ""8. Smoothness of Sa???Refinable Functions and Consequences""; ""8.1. Determining smoothness of the refinahle function using differenced subdivision schemes""; ""8.2. Subdivision schemes with smooth refinahle functions generate polynomials""; ""8.3. Univariate subdivision schemes producing piecewise polynomial functions""; ""9. Appendix""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 93, Number 453. 606 $aSpline theory 606 $aAlgorithms 606 $aComputer graphics 608 $aElectronic books. 615 0$aSpline theory. 615 0$aAlgorithms. 615 0$aComputer graphics. 676 $a511/.42 700 $aCavaretta$b Alfred S.$f1944-$0903058 702 $aDahmen$b Wolfgang$f1949- 702 $aMicchelli$b Charles A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480572403321 996 $aStationary subdivision$92018742 997 $aUNINA