% plot the error polynomial on [a,b]

a = -1;
b =  1;

% points for visualization
Xf = linspace(a,b,500);
figure(1); clf;
fs = 24; %font size

for N = 2:100,
    % interpolation points
    Xb = linspace(-1,1,N);
    
    % form the polynomial
    % (x-x1)*(x-x2)*...*(x-xN)
    p = @(x) prod(x-Xb);
    % evaluate at the visualization points
    pf = arrayfun(p,Xf);
    maxpf = max(abs(pf));
    
    % visualize
    plot(Xf,pf,'-', ...
         Xb,zeros(size(Xb)),'x', ...
         'LineWidth',3,'MarkerSize',10);
    xlabel('x','FontSize',fs); ylabel('y','FontSize',fs); 
    axis([a, b,-maxpf,maxpf]); grid on;
    title(sprintf('Interpolation using %3d points',N),'FontSize',fs);
    pause;
end