% Question 4.
% Parts b and c. Using monomial basis...
figure(1)
x = [0 0.5 1];
V = vander(x);
y = exp(x)';
c = V\y;

% c =
%   0.841678574117578
%   0.876603254341467
%   1.000000000000000

x_vals = linspace(0,1,50);
y_vals = exp(x_vals);
plot(x_vals,y_vals);
hold on
y_est = polyval(c,x_vals);
plot(x_vals,y_est,'r');

% Part d - plot absolute error.
figure(2)
semilogy(abs(y_vals - y_est))