% Illustration of the runge phenomenon

for k = [5,11,25,51,75]
   
   shg % bring plot window forward
   x = linspace(-1,1,k); % generate k nodes (odd number)
   y = 1 ./ (1 + 25*x.^2);
   
   xx = linspace(-1,1,200); % generate many points on curve
   yr = 1 ./ (1 + 25*xx.^2);
   
   p = polyfit(x,y,k-1);    % generate points for polynomial
   yp = polyval(p, xx);
   yr = 1 ./ (1 + 25*xx.^2);
   
   plot(x,y,'o',  ...  % show k nodes on curve
      xx,yp,'-',  ...  % show the degree k-1 polynomial
      xx,yr,'--')      % show the curve with dotted line
   axis([-1,1,-0.5,2]);
   input('press enter');
end