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The Kink Phenomenon in Fejér and Clenshaw-Curtis Quadrature

Abstract:

The Fejér and Clenshaw-Curtis rules for numerical integration exhibit a curious phenomenon when applied to certain analytic functions. When N, (the number of points in the integration rule) increases, the error does not decay to zero evenly but does so in two distinct stages. For N less than a critical value, the error behaves like $O(\varrho^{-2N})$, where $\varrho$ is a constant greater than 1. For these values of N the accuracy of both the Fejér and Clenshaw-Curtis rules is almost indistin...

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Publication date:
2006-09-05
URN:
uuid:a4277453-1a92-4bd7-bbca-d8764af572f2
Local pid:
oai:eprints.maths.ox.ac.uk:1107

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