% Lagrange-Interpolation von sin auf dem Intervall [0,2*pi]

a = 0; b = 2*pi;
xmany = linspace(a,b,500);
for n = 2:2:20,
   x = linspace(a,b,n+1);
   y = sin(x);
   ymany = sin(xmany);
   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 = (1 + cos( ( 2*(1:n)-1 ) / 2 / n * pi ))*pi;
   y = sin(x);
   ymany = sin(xmany);
   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