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.
CACM May, 1972
Gentleman, W. M.
