BIT Numerical Mathematics

, Volume 37, Issue 1, pp 232–236 | Cite as

A de Casteljau algorithm for generalized Bernstein polynomials

  • George M. Phillips
Scientific Notes


This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case.

AMS subject classification


Key words

Bernstein polynomial de Casteljau algorithm 


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  1. 1.
    G. E. Andrews,The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.Google Scholar
  2. 2.
    E. W. Cheney,Introduction to Approximation Theory, McGraw-Hill, New York, 1966.MATHGoogle Scholar
  3. 3.
    P. J. Davis,Interpolation and Approximation, Dover, New York, 1976.MATHGoogle Scholar
  4. 4.
    J. Hoschek and D. Lasser,Fundamentals of Computer-Aided Geometric Design, A. K. Peters, Wellesley, Mass., 1993.MATHGoogle Scholar
  5. 5.
    S. L. Lee and G. M. Phillips,Polynomial interpolation at points of a geometric mesh on a triangle, Proc. Roy. Soc. Edin., 108A (1988), pp. 75–87.MathSciNetGoogle Scholar
  6. 6.
    G. M. Phillips,Bernstein polynomials based on the q-integers, in Festschrift for T. J. Rivlin (in press).Google Scholar
  7. 7.
    T. J. Rivlin,An Introduction to the Approximation of Functions, Dover, New York, 1981.MATHGoogle Scholar
  8. 8.
    I. J. Schoenberg,On polynomial interpolation at the points of a geometric progression, Proc. Roy. Soc. Edin., 90A (1981), pp. 195–207.MathSciNetGoogle Scholar

Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • George M. Phillips
    • 1
  1. 1.Mathematical InstituteUniversity of St AndrewsFifeSt AndrewsScotland

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