Fast Construction of the Fejér and
Clenshaw-Curtis Quadrature Rules

by Jörg Waldvogel, Seminar for Applied Mathematics,
Swiss Federal Institute of Technology ETH,
CH-8092 Zürich, Switzerland


We present an elegant algorithm for stably and quickly generating the weights of Fejér's quadrature rules and of the Clenshaw-Curtis rule. The weights for an arbitrary number of nodes are obtained as the discrete Fourier transform of an explicitly defined vector of rational or algebraic numbers. Since these rules have the capability of forming nested families, some of them have gained renewed interest in connection with quadrature over multi-dimensional regions.

Download complete paper (10 pages), BIT Numerical Mathematics 46 (2006), 195-202 : fejer.pdf

Presentation (24 frames), Chebfun and Beyond, September 17 - 20, 2012, Oxford UK: oxford.pdf