BIT Numerical Mathematics

, Volume 46, Issue 1, pp 195–202 | Cite as

Fast Construction of the Fejér and Clenshaw–Curtis Quadrature Rules

Article

Abstract

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.

Key words

numerical quadrature Fejér’s quadrature rules Clenshaw–Curtis quadrature discrete Fourier transform 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Seminar for Applied MathematicsSwiss Federal Institute of Technology ETHZurichSwitzerland

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