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Symbols and exact regularity of symmetric pseudo-splines of any arity

Symbols and exact regularity of symmetric pseudo-splines of any arity

Category
Academic article
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 Hölder 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.
Client
  • Research Council of Norway (RCN) / prosjektnummer 222335
  • Research Council of Norway (RCN) / PROSJEKTNUMMER 222335
Language
English
Author(s)
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics