BIT Numerical Mathematics

, Volume 44, Issue 1, pp 63–78

Generalized Bernstein Polynomials

  • Stanisław Lewanowicz
  • Paweł Woźny
Article

Abstract

We introduce polynomials Bni(x;ω|q), depending on two parameters q and ω, which generalize classical Bernstein polynomials, discrete Bernstein polynomials defined by Sablonnière, as well as q-Bernstein polynomials introduced by Phillips. Basic properties of the new polynomials are given. Also, formulas relating Bni(x;ω|q), big q-Jacobi and q-Hahn (or dual q-Hahn) polynomials are presented.

generalized Bernstein polynomials generalized Bézier form generalized de Casteljau algorithm degree elevation big q-Jacobi polynomials q-Hahn polynomials dual q-Hahn polynomials orthogonal polynomial expansion 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Stanisław Lewanowicz
    • 1
  • Paweł Woźny
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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