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

Algorithm 4

function a = fejer1dct(f,N)            % coefficients for Fejér’s  second rule

x = cos(pi(2(0:N)’+1)/(2*N+2));         % The first kind of Chebyshev points

fx = feval(f,x);                   %  f  evaluated at these points

a = dct(fx)sqrt(2/(N+1));a(1)=a(1)/sqrt(2);    % Chebyshev coefficients