Three term recurrence for the evaluation of multivariate orthogonal polynomials

DOI10.1016/j.jat.2009.07.005zbMath1190.33011OpenAlexW2076361070MaRDI QIDQ2268566

Roberto Barrio, Thomas Sauer, Juan Manuel Peña

Publication date: 8 March 2010

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2009.07.005

zbMATH Keywords

recurrence relationsmultivariate orthogonal polynomialsevaluation algorithms

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (5)

Generalized white noise analysis and topological algebras ⋮ Multivariate orthogonal polynomials and integrable systems ⋮ A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials ⋮ Recursive three-term recurrence relations for the Jacobi polynomials on a triangle ⋮ On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions

Uses Software

• mctoolbox
• OPQ
• MOPS

Cites Work

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• Jacobi polynomials in Bernstein form
• A unified rounding error bound for polynomial evaluation
• Weak classical orthogonal polynomials in two variables
• Monomial orthogonal polynomials of several variables
• Numerical evaluation of the \(p\)th derivative of Jacobi series
• Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
• MOPS: multivariate orthogonal polynomials (symbolically)
• A semiclassical perspective on multivariate orthogonal polynomials
• The Recursion Formulas for Orthogonal Polynomials innVariables
• Orthogonality and Recursion Formulas for Polynomials in n Variables
• Recurrence Formulas for Multivariate Orthogonal Polynomials
• Accuracy and Stability of Numerical Algorithms
• On Multivariate Orthogonal Polynomials
• Orthogonal Polynomials of Several Variables
• Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series

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