Algorithm 424: Clenshaw-Curtis quadrature [D1]
Communications of the ACM
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
Remark on algorithm 351 [D1]: modified Romberg quadrature
Communications of the ACM
Algorithm 351: modified Romberg quadrature
Communications of the ACM
Certification of Algorithm 279: Chebyshev quadrature
Communications of the ACM
Algorithm 279: Chebyshev quadrature
Communications of the ACM
Algorithm 424: Clenshaw-Curtis quadrature [D1]
Communications of the ACM
Algorithm 479: A minimal spanning tree clustering method
Communications of the ACM
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
Remark on algorithm 400: modified Håvie integration
Communications of the ACM
On the Check of Accuracy of the Coefficients of Formal Power Series
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Fluctuationlessness theorem to approximate univariate functions' matrix representations
WSEAS Transactions on Mathematics
Simulation-based optimal Bayesian experimental design for nonlinear systems
Journal of Computational Physics
Fast construction of Fejér and Clenshaw-Curtis rules for general weight functions
Computers & Mathematics with Applications
ACM Transactions on Mathematical Software (TOMS)
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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.