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Symbols and exact regularity of symmetric pseudo-splines of any arity
- Source :
- Bit Numerical Mathematics 57 (3), pp. 867 -- 900 (2017)
- Publication Year :
- 2016
-
Abstract
- Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc-Deslauriers schemes and B-spline schemes. Using a generating function approach, we derive expressions for the symbols of the symmetric $m$-ary pseudo-spline subdivision schemes. We show that their masks have positive Fourier transform, making it possible to compute the exact H\"older regularity algebraically as a logarithm of the spectral radius of a matrix. We apply this method to compute the regularity explicitly in some special cases, including the symmetric binary, ternary, and quarternary pseudo-spline schemes.<br />Comment: 31 pages
Details
- Database :
- arXiv
- Journal :
- Bit Numerical Mathematics 57 (3), pp. 867 -- 900 (2017)
- Publication Type :
- Report
- Accession number :
- edsarx.1611.00618
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10543-017-0656-y