% Script file:  Same as before, except using Chebyshev points

f=inline('1./(1+12*x.^2)');
%% Example 1:  Seven points
%First define the points for the polynomial:
n=7;
xp=cos(((2*(1:n)-1)*pi)./(2*n));
yp=f(xp);

%Find the coefficients:
[v,c]=newtdd(xp,yp);
xx=linspace(-1,1,200);  %Pts for f, P
yy1=f(xx);
yy2=nest(c,xx,xp);
plot(xp,yp,'r*',xx,yy1,xx,yy2);
legend('Data','f(x)','Polynomial')

%% Example 2:  15 Points
n=15;
xp=cos(((2*(1:n)-1)*pi)./(2*n));
yp=f(xp);

%Find the coefficients:
[v,c]=newtdd(xp,yp);
xx=linspace(-1,1,200);  %Pts for f, P
yy1=f(xx);
yy2=nest(c,xx,xp);
plot(xp,yp,'r*',xx,yy1,xx,yy2);
axis([-1 1 -1 2])
legend('Data','f(x)','Polynomial')

%% Example 3:  25 Points
n=25;
xp=cos(((2*(1:n)-1)*pi)./(2*n));
yp=f(xp);

%Find the coefficients:
[v,c]=newtdd(xp,yp);
xx=linspace(-1,1,200);  %Pts for f, P
yy1=f(xx);
yy2=nest(c,xx,xp);
plot(xp,yp,'r*',xx,yy1,xx,yy2);
axis([-1 1 -1 2])
legend('Data','f(x)','Polynomial')

%% Error from Example 3:
plot(yy1-yy2);
title('Error using 25 points:  Chebyshev')