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 language | English |
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Pages (from-to) | 305-322 |
Number of pages | 18 |
Journal | Constructive Approximation |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1985 |
Keywords
- AMS classification: 41A15
- Box spline
- Control net
- Convergence rate
- Subdivision algorithms