On convergence rates of Fejér and Gauss–Chebyshev quadrature rules

This paper presents convergence rates for Fejér’s first and second rules for functions of limited regularities. From these results together with the convergence rates on Gauss and Clenshaw–Curtis quadratures, we see that for functions of limited regularities, Gauss, Clenshaw–Curtis and Fejér’s quadratures are of approximately equal accuracy for I [ f ] = ∫ − 1 1 f ( x ) d x . In addition, building on the aliasing errors and the decays of the coefficients in the Chebyshev expansion of f , sharp convergence rates are also obtained for Gauss–Chebyshev quadrature.