Fast construction of Fejér and Clenshaw–Curtis rules for general weight functions

The main purpose of this paper is to compute the weights of Clenshaw–Curtis and Fejér type quadrature rules via DCT and DST, for general weight functions w. The approach is different from that used by Waldvogel (2006) in [10], where the author considered the computation of these sets only for the Le...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2013-02, Vol.65 (4), p.682-693
Main Author: Sommariva, Alvise
Format: Article
Language:English
Subjects:
Clenshaw–Curtis rules
Computation
Discrete Cosine Transform
Discrete Sine Transform
Fejér rules
Gegenbauer weight function
Trigonometric quadrature
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Summary:The main purpose of this paper is to compute the weights of Clenshaw–Curtis and Fejér type quadrature rules via DCT and DST, for general weight functions w. The approach is different from that used by Waldvogel (2006) in [10], where the author considered the computation of these sets only for the Legendre weight w≡1 using DFT arguments.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2012.12.004