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arXiv · 1401.0638

Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities

Haiyong Wang
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Abstract

In this paper, we investigate the rate of convergence of Clenshaw-Curtis quadrature and its acceleration for functions with endpoint singularities in X^s, where X^s denotes the space of functions whose Chebyshev coefficients decay asymptotically as a_k = O(k^{-s-1}) for some positive s. For such unctions, we show that the convergence rate of (n + 1)-point Clenshaw-Curtis quadrature is O(n^{-s-2}). Furthermore, an asymptotic error expansion for Clenshaw-Curtis quadrature is presented which enables us to employ some extrapolation techniques to accelerate its convergence. Numerical examples are provided to confirm our analysis.

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Haiyong Wang. 2014-01-03. Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities. https://arxiv.org/abs/1401.0638

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