Orthogonal Polynomials on Planar Cubic Curves

Orthogonal Polynomials on Planar Cubic Curves

Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that...

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Bibliographic Details
Published in:Foundations of computational mathematics Vol. 23; no. 1; pp. 1 - 31
Main Authors: Fasondini, Marco, Olver, Sheehan, Xu, Yuan
Format: Journal Article
Language:English
Published: New York Springer US 01-02-2023
Springer
Springer Nature B.V
Subjects:
Applications of Mathematics
Computer Science
Differential equations
Economics
Functions, Orthogonal
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical analysis
Mathematical research
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Polynomials
Singularity (mathematics)
Weighting functions
United Kingdom
Orthogonal series
42C10
Approximation
65M70
Orthogonal polynomials
Singular functions
33C50
Cubic curve
42C05
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Summary:Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that these orthogonal polynomials can be used to approximate functions with cubic and square root singularities, and demonstrate their usage for solving differential equations with singular solutions.
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-021-09540-w