Constructive Approximation

, Volume 15, Issue 3, pp 381–426 | Cite as

Regularity of Irregular Subdivision

  • I. Daubechies
  • I. Guskov
  • W. Sweldens
Article

Abstract.

We study the smoothness of the limit function for one-dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midway as is usually the case. For the natural generalization of the four-point scheme introduced by Dubuc and Dyn, Levin, and Gregory, we show that, under some geometric restrictions, the limit function is always C1; under slightly stronger restrictions we show that the limit function is almost C2 , the same regularity as in the regularly spaced case.

Key words. Regularity, Irregular samples, Subdivision, Interpolation, Scaling function, Wavelet. AMS Classification. 41A05, 65Y25, 26A16, 65905. 

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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • I. Daubechies
    • 1
  • I. Guskov
    • 2
  • W. Sweldens
    • 3
  1. 1.Program for Applied and Computational Mathematics Princeton UniversityPrincetonUSA
  2. 2.Program for Applied and Computational Mathematics Princeton UniversityPrincetonUSA
  3. 3.Lucent Technologies Bell LaboratoriesUSA

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