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

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