mlab

function [ p ] = upp2a( n )

f = @(x) 1 ./ (1 + 8.*(x - 1/9).^2);
h = 4 / (n-1);
xi = @(i,n) -2 + 4*(i-1)/(n-1);

x = xi(1,n):h:xi(n,n);
y = f(x)';

A = vander(x);
c = (A\y);

p = @(x) polyval(c,x);

end










n = 7;

f = @(x) 1 ./ (1 + 8.*(x - 1/9).^2);
h = 4 / (n-1);
xi = @(i,n) -2 + 4*(i-1)/(n-1);

x = xi(1,n):h:xi(n,n);
y = f(x)';

xx = xi(1,n):0.01:xi(n,n);

mypoly = upp2a(n);
linearpoly = interp1(x,y,xx);
splinepoly = spline(x,y,xx);

xx = xi(1,n):0.01:xi(n,n);

figure(1);
plot(xx,mypoly(xx));
figure(2);
plot(xx,linearpoly);
figure(3);
plot(xx,splinepoly);