Recurrence relations for orthogonal polynomials on triangular domains

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In Farouki et al, 2003, Legendre-weighted orthogonal polynomials Pn,r(u, v,w), r = 0, 1, . . ., n, n ≥ 0 on the triangular domain T = {(u, v,w): u, v,w ≥ 0, u+v+w = 1} are constructed, where u, v,w are the barycentric coordinates. Unfortunately, evaluating the explicit formulas requires many operations and is not very practical from an algorithmic point of view. Hence, there is a need for a more efficient alternative. A very convenient method for computing orthogonal polynomials is based on recurrence relations. Such recurrence relations are described in this paper for the triangular orthogonal polynomials, providing a simple and fast algorithm for their evaluation.

Original languageEnglish
Article number25
Issue number2
Publication statusPublished - Jun 1 2016
Externally publishedYes


  • Bernstein polynomials
  • Bivariate orthogonal polynomials
  • Legendre polynomials
  • Recurrence relation
  • Triangular domains

ASJC Scopus subject areas

  • General Mathematics


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