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Recurrence Relations for Orthogonal Polynomials on Triangular Domains

Author

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  • Abedallah Rababah

    (Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan)

Abstract

In Farouki et al , 2003, Legendre-weighted orthogonal polynomials P n , 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.

Suggested Citation

  • Abedallah Rababah, 2016. "Recurrence Relations for Orthogonal Polynomials on Triangular Domains," Mathematics, MDPI, vol. 4(2), pages 1-7, April.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:2:p:25-:d:68094
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