By W. Morven Gentleman
Communications of the ACM,
Vol. 15 No. 5, Pages 337-342
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.
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