Recurrence relations for orthogonal polynomials on triangular domains
type: Item
instance of: scholarly article
title: Recurrence relations for orthogonal polynomials on triangular domains
zbMATH Open document ID: 1360.65081
author: Abedallah Rababah
published in: Mathematics
publication date: 2017-03-16T00:00:00Z
review text: Summary: In Farouki et al. (2003), Legendre-weighted orthogonal polynomials \(\mathcal P_{n,r}(u,v,w)\), \(r=0,1,\dots,n\), \(n\geq 0\) on the triangular domain \(T=\{(u,v,w):u,v,w\geq 0,u+v+w=1\}\) 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.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33F05
Mathematics Subject Classification ID: 65Q30
zbMATH DE Number: 6695451
zbMATH Keywords: recurrence relation
zbMATH Keywords: bivariate orthogonal polynomials
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: triangular domains
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: math4020025
OpenAlex ID: W2339095077
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DOI: 10.3390/MATH4020025
description: scientific article; zbMATH DE number 6695451