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Numerical Algorithms

, Volume 42, Issue 2, pp 171–179 | Cite as

Computing orthogonal polynomials on a triangle by degree raising

  • Shayne Waldron
Article
  • 94 Downloads

Abstract

We give an algorithm for computing orthogonal polynomials over triangular domains in Bernstein–Bézier form which uses only the operator of degree raising and its adjoint. This completely avoids the need to choose an orthogonal basis (or tight frame) for the orthogonal polynomials of a given degree, and hence the difficulties inherent in that approach. The results are valid for Jacobi polynomials on a simplex, and show the close relationship between the Bernstein form of Jacobi polynomials, Hahn polynomials and degree raising.

Keywords

Bernstein–Bézier form Hahn polynomials Jacobi polynomials surface smoothing 

AMS (MOS) Subject Classifications

primary 33C45 65D17 secondary 41A10 

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References

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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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