Clenshaw-Curtis
Implementing Clenshaw-Curtis quadrature, I methodology and experience. Clenshaw-Curtis quadrature is a particularly important automatic quadrature scheme for a variety of reasons, especially the high accuracy obtained from relatively few integrand values. However, it has received little use because it requires the computation of a cosine transformation, and the arithmetic cost of this has been prohibitive. This paper is in two parts; a companion paper, “II Computing the Cosine Transformation,” shows that this objection can be overcome by computing the cosine transformation by a modification of the fast Fourier transform algorithm. This first part discusses the strategy and various error estimates, and summarizes experience with a particular implementation of the scheme.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 43 articles )
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Sorted by year (- Nakatsukasa, Yuji; Townsend, Alex: Error localization of best (L_1) polynomial approximants (2021)
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- Gilles, Marc Aurèle; Townsend, Alex: Continuous analogues of Krylov subspace methods for differential operators (2019)
- Hasegawa, Takemitsu; Sugiura, Hiroshi: Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm (2019)
- Liu, Guidong; Xiang, Shuhuang: Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels (2019)
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- Townsend, Alex; Webb, Marcus; Olver, Sheehan: Fast polynomial transforms based on Toeplitz and Hankel matrices (2018)
- Wang, Haiyong: On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities (2018)
- Xiang, Shuhuang; Li, Bin; Liu, Guidong: On efficient computation of highly oscillatory retarded potential integral equations (2018)
- Hasegawa, Takemitsu; Sugiura, Hiroshi: A user-friendly method for computing indefinite integrals of oscillatory functions (2017)
- Lewanowicz, Stanisław; Keller, Paweł; Woźny, Paweł: Constrained approximation of rational triangular Bézier surfaces by polynomial triangular Bézier surfaces (2017)
- Motygin, Oleg V.: Numerical approximation of oscillatory integrals of the linear ship wave theory (2017)
- Ruijter, M. J.; Oosterlee, C. W.: A Fourier cosine method for an efficient computation of solutions to BSDEs (2015)
- Domínguez, V.; Graham, I. G.; Smyshlyaev, V. P.: Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals (2011)
- Hasegawa, Takemitsu; Sugiura, Hiroshi: Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives (2011)
- Sugiura, Hiroshi; Hasegawa, Takemitsu: A polynomial interpolation process at quasi-Chebyshev nodes with the FFT (2011)
- Keller, Paweł; Woźny, Paweł: On the convergence of the method for indefinite integration of oscillatory and singular functions (2010)