X-Nico

unusual facts about trapezoidal rule



Clenshaw–Curtis quadrature

Unlike computation of arbitrary integrals, however, Fourier-series integrations for periodic functions (like f(\cos\theta), by construction), up to the Nyquist frequency k=N, are accurately computed by the N+1 equally spaced and equally weighted points \theta n = n \pi / N for n = 0,\ldots,N (except the endpoints are weighted by 1/2, to avoid double-counting, equivalent to the trapezoidal rule or the Euler–Maclaurin formula).


see also