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On the convergence rates of subdivision algorithms for box spline surfaces

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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).

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 4800, Bielefeld, West Germany

    Wolfgang Dahmen

  2. School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, 69978, Tel-Aviv, Israel

    Nira Dyn & David Levin

Authors
  1. Wolfgang Dahmen
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  2. Nira Dyn
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  3. David Levin
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Additional information

Communicated by Charles A. Micchelli.

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Dahmen, W., Dyn, N. & Levin, D. On the convergence rates of subdivision algorithms for box spline surfaces. Constr. Approx 1, 305–322 (1985). https://doi.org/10.1007/BF01890038

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  • DOI: https://doi.org/10.1007/BF01890038

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