2355	 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. Clenshaw Curtis numerical integration automatic quadrature error estimates Chebyshev series
