Constructive Approximation

, Volume 4, Issue 1, pp 265–288 | Cite as

Urn models and B-splines

  • Ronald N. Goldman


Urn models are used to construct normalized B-spline basis functions over arbitrary knot vectors. These stochastic models are then applied to derive some of the basic analytic properties of B-splines. In particular, the Cox-de Boor recursion formula is given a probabilistic interpretation. The connection between urn models, B-splines, and Beta-splines is also discussed.

AMS classification

41A15 60C05 

Keywords and phrases

B-spline Beta-spline Urn model 


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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Ronald N. Goldman
    • 1
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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