On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules

Algorithm 1

function  a  =  clenshaw_curtis(f,N)                     %  (N+1)-coefficients for  C-C quadrature

x  =  cos(pi(0:N)’/N);                     %  C-C  points

fx  =  feval(f,x)/(2*N);                         %  f  evaluated at these points

g  =  fft(fx([1:N+1  N:−1:2]));                 %  FFT

a  =  [g(1);  g(2:N)+g(2N:−1:N+2);  g(N+1)];            %  Chebyshev coefficients