Orthogonal polynomials on planar cubic curves
File(s)
Published version
Author(s)
Fasondini, Marco
Olver, Sheehan
Xu, Yuan
Type
Journal Article
Abstract
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.
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.
Date Issued
2023-02-01
Date Acceptance
2021-07-30
Citation
Foundations of Computational Mathematics, 2023, 23, pp.1-31
ISSN
1615-3375
Publisher
Springer Verlag
Start Page
1
End Page
31
Journal / Book Title
Foundations of Computational Mathematics
Volume
23
Copyright Statement
© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://link.springer.com/article/10.1007/s10208-021-09540-w
Publication Status
Published
Date Publish Online
2021-11-11