% Runge with Chebychev nodes
function interp_runge_cheby
   	n = 7
	i = 1:n;
	theta = (2*i-1)*pi/2/n;
	x = cos(theta);
	y = runge(x);
	plot(x,y,'k*'); hold on;

	n = numel(x);
	c = newtdd(x,y,n);
	
	xx = linspace(x(1),x(n),400);
	plot(xx,runge(xx),'b');
	yy = nest(n-1,c,xx,x);
	plot(xx,yy,'r'); 
	title('Runge function (blue) and poly interpolant (red) with Cheby nodes');
	hold off;
end

function y = runge(x)
	y = 1./(1+12*x.^2);
end