Asymptotically optimal quadrature rules for uniform splines over the real line

Rachid Ait-Haddou; Helmut Ruhland

doi:10.1007/s11075-020-00929-2

Asymptotically optimal quadrature rules for uniform splines over the real line

Rachid Ait-Haddou^*, Helmut Ruhland

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We provide explicit asymptotically optimal quadrature rules for uniform C^k-splines, k = 0,1, over the real line. The nodes of these quadrature rules are given in terms of the zeros of ultraspherical polynomials (Gegenbauer polynomials) and related polynomials. We conjecture that our derived rules are the only possible periodic asymptotically optimal quadrature rules for these spline spaces.

Original language	English
Pages (from-to)	1189-1223
Number of pages	35
Journal	Numerical Algorithms
Volume	86
Issue number	3
DOIs	https://doi.org/10.1007/s11075-020-00929-2
State	Published - Mar 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

B-splines
Gegenbauer polynomials
Isogeometric analysis
Near-Gaussian quadrature
Optimal quadrature rules

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-020-00929-2

Cite this

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abstract = "We provide explicit asymptotically optimal quadrature rules for uniform Ck-splines, k = 0,1, over the real line. The nodes of these quadrature rules are given in terms of the zeros of ultraspherical polynomials (Gegenbauer polynomials) and related polynomials. We conjecture that our derived rules are the only possible periodic asymptotically optimal quadrature rules for these spline spaces.",

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KW - B-splines

KW - Gegenbauer polynomials

KW - Isogeometric analysis

KW - Near-Gaussian quadrature

KW - Optimal quadrature rules

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M3 - Article

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Asymptotically optimal quadrature rules for uniform splines over the real line

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this