% Lagrange-Interpolation der Runge-Funktion auf dem Intervall [-1,1]
a = -1; b = 1;
xmany = linspace(a,b,500);
for n = 2:2:30,
   x = linspace(a,b,n+1);
   y = 1./(1+25*x.^2);
   ymany = 1./(1+25*xmany.^2);
   lambda = baryzentrisch(x);
   p = baryzentrischauswertung(x,xmany,y,lambda);
   subplot(2,2,1);
   plot(xmany,ymany,'b-',xmany,p,'r-');
   makelarge
   title(sprintf('Gleichverteilt, Polynomgrad %i',n));
   subplot(2,2,3);
   semilogy(xmany,abs(ymany-p),'r-');
   makelarge
   title('Interpolationsfehler');

   x = cos( ( 2*(1:n)-1 ) / 2 / n * pi );
   y = 1./(1+25*x.^2);
   ymany = 1./(1+25*xmany.^2);
   lambda = baryzentrisch(x);
   p = baryzentrischauswertung(x,xmany,y,lambda);
   subplot(2,2,2);
   plot(xmany,ymany,'b-',xmany,p,'r-');
   makelarge
   title(sprintf('Chebyshev, Polynomgrad %i',n));
   subplot(2,2,4);
   semilogy(xmany,abs(ymany-p),'r-');
   makelarge
   title('Interpolationsfehler');
   pause
end