Recurrence Relations for Orthogonal Polynomials on Triangular Domains

Abedallah Rababah
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Abedallah Rababah: Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan

Mathematics, 2016, vol. 4, issue 2, 1-7

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.

Keywords: recurrence relation; bivariate orthogonal polynomials; Bernstein polynomials; Legendre polynomials; triangular domains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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