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Orthogonal polynomials in and on a quadratic surface of revolution
File(s)
paper.pdf (2.14 MB)
Accepted version
Author(s)
Olver, Sheehan
Xu, Yuan
Type
Journal Article
Abstract
We present explicit constructions of orthogonal polynomials insidequadratic bodies of revolution, including cones, hyperboloids, and paraboloids.We also construct orthogonal polynomials on the surface of quadratic surfaces ofrevolution, generalizing spherical harmonics to the surface of a cone, hyperboloid,and paraboloid. We use this construction to develop cubature and fast approxi-mation methods.
Date Issued
2020-06-05
Date Acceptance
2020-03-01
Citation
Mathematics of Computation, 2020, 89 (326), pp.2848-2865
URI
URL
DOI
ISSN
0025-5718
Publisher
American Mathematical Society
Start Page
2848
End Page
2865
Journal / Book Title
Mathematics of Computation
Volume
89
Issue
326
Copyright Statement
© 2020 American Mathematical Society. License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use
Sponsor
The Leverhulme Trust
Identifier
https://www.ams.org/journals/mcom/2020-89-326/S0025-5718-2020-03544-3/
Grant Number
RPG-2019-144
Subjects
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Numerical & Computational Mathematics
Publication Status
Published
Date Publish Online
2020-06-05