p30c.m

% p30c.m - spectral integration, Gauss style (compare p30.m)

% Computation: various values of N, four functions:
  Nmax = 50; E = zeros(4,Nmax); clf
  for N = 1:Nmax;
    [x,w] = gauss(N);
    f = abs(x).^3;     E(1,N) = abs(w*f - .5);
    f = exp(-x.^(-2)); E(2,N) = abs(w*f - ...
                           2*(exp(-1)+sqrt(pi)*(erf(1)-1)));
    f = 1./(1+x.^2);   E(3,N) = abs(w*f - pi/2);
    f = x.^10;         E(4,N) = abs(w*f - 2/11);
  end

% Plot results:
  labels = {'|x|^3','exp(-x^{-2})','1/(1+x^2)','x^{10}'};
  for iplot = 1:4, 
    subplot(3,2,iplot)
    semilogy(E(iplot,:)+1e-100,'.','markersize',12), hold on
    semilogy(E(iplot,:)+1e-100)
    axis([0 Nmax 1e-18 1e3]), grid on
    set(gca,'xtick',0:10:Nmax,'ytick',(10).^(-15:5:0))
    ylabel error, text(32,.004,labels(iplot))
  end