On the convergence rates of subdivision algorithms for box spline surfaces

Wolfgang Dahmen*, Nira Dyn, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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).

Original languageEnglish
Pages (from-to)305-322
Number of pages18
JournalConstructive Approximation
Volume1
Issue number1
DOIs
StatePublished - Dec 1985

Keywords

  • AMS classification: 41A15
  • Box spline
  • Control net
  • Convergence rate
  • Subdivision algorithms

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