%Script file to show the Runge phenomenon (p 158-159 of our text)

n=15;                  %Number of base points
xf=linspace(-1,1,n);   %get n equally spaced points between +/-1
xx=linspace(-1,1,200); %Data to plot
f=inline('1./(1+12*x.^2)');

yf=f(xf);  %These will be the y-data for the polynomial
yy=f(xx);  % y-data to plot for the function f (not the polynomial approx)

coefs=newtdd(xf,yf);
cy=nest(n-1,coefs,xx,xf);

plot(xf,yf,'k*',xx,yy,'b-',xx,cy,'r-');
legend('Data','Actual Function','Poly Approx');