Orthogonal polynomials on a class of planar algebraic curves
File(s)Stud Appl Math - 2023 - Fasondini.pdf (806.33 KB)
Published version
Author(s)
Fasondini, Marco
Olver, Sheehan
Xu, Yuan
Type
Journal Article
Abstract
We construct bivariate orthogonal polynomials (OPs) on algebraic
curves of the form ym = φ(x) in R2 where m = 1, 2 and φ is a polynomial of arbitrary degree d, in terms of univariate semiclassical OPs. We compute connection
coefficients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix
is shown to be banded and the connection coefficients and Jacobi matrices for OPs
of degree 0, . . . , N are computed via the Lanczos algorithm in O(Nd4) operations.
curves of the form ym = φ(x) in R2 where m = 1, 2 and φ is a polynomial of arbitrary degree d, in terms of univariate semiclassical OPs. We compute connection
coefficients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix
is shown to be banded and the connection coefficients and Jacobi matrices for OPs
of degree 0, . . . , N are computed via the Lanczos algorithm in O(Nd4) operations.
Date Issued
2023-07-01
Date Acceptance
2023-04-19
Citation
Studies in Applied Mathematics, 2023, 151 (1), pp.369-405
ISSN
0022-2526
Publisher
Wiley
Start Page
369
End Page
405
Journal / Book Title
Studies in Applied Mathematics
Volume
151
Issue
1
Copyright Statement
© 2023 The Authors. Studies in Applied Mathematics published by Wiley Periodicals LLC.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
https://onlinelibrary.wiley.com/doi/full/10.1111/sapm.12582
Publication Status
Published
Date Publish Online
2023-05-08