clear
disp('Quadratic curve fit via least squares')
A = [ 1 1 1;4 2 1;9 3 1;16 4 1;25 5 1]
pause
d = [1 5 8 17 26]'
pause
disp('Use the inverse matrix to solve the normal equations')
sol1 = inv(A'*A)*(A'*d)
pause
disp('Use Gauss elimination via \ to solve the normal equations')
sol2 = (A'*A)\(A'*d)
pause
disp('Use the QR factoriztion of A via A\d')
sol3 = A\d
pause
disp('Compare the quadratic and linear approximation')
disp('Linear approximatin via A(:,2:3)\d')
pause
sol_lin = A(:,2:3)\d
sol_quad = A\d
pause
res_lin = (d - A(:,2:3)*sol_lin)'*(d - A(:,2:3)*sol_lin)
res_quad = (d - A*sol_quad)'*(d - A*sol_quad)
pause
x = 1:1:5
pause
ls_lin = sol_lin(1)*x + sol_lin(2)
ls_quad = sol_quad(1)*x.^2 +sol_quad(2)*x + sol_quad(3)
plot(x,d,'*',x,ls_lin,x, ls_quad)