Constructive Approximation

, Volume 1, Issue 1, pp 305–322

On the convergence rates of subdivision algorithms for box spline surfaces

  • Wolfgang Dahmen
  • Nira Dyn
  • David Levin

DOI: 10.1007/BF01890038

Cite this article as:
Dahmen, W., Dyn, N. & Levin, D. Constr. Approx (1985) 1: 305. doi:10.1007/BF01890038


Dahmen and Micchelli [8] have shown that in general the coefficients of the refined control nets of a box spline surface converge to the surface at (at least) the rate of the refinement. The purpose of this article is to show that under mild additional assumptions the convergence rate is even quadratic. Although this rate is in general best possible, we point out under what circumstances even higher rates are obtained (locally).

AMS classification


Key words and phrases

Box splineConvergence rateSubdivision algorithmsControl net

Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • Wolfgang Dahmen
    • 1
  • Nira Dyn
    • 2
  • David Levin
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldWest Germany
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel-AvivIsrael