1. Implementing Clenshaw-Curtis Quadrature, I Methodology and Experience.
- Author
-
timlake, W. P. and Gentleman, W. Morven
- Subjects
- *
NUMERICAL integration , *COMPUTER systems , *ALGORITHMS , *COMPUTER science , *NUMERICAL analysis , *ARITHMETIC - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 1972