%  demo_fd.m
%
%  Demonstrate effect of floating point arithmetic on divided difference 
%  approximations to the derivative of f(x) = exp(x) at x0=1.

  h = 1;  n = 70;
  x0 = 1;
  expx0 = exp(x0);
  hvec = zeros(n,1);
  evec = zeros(n,1);
  true_deriv = expx0;
  for i = 1:n
    ddif = (exp(x0+h) - expx0)/h;       %  Compute divided difference approx.
    abs_error = abs(ddif - true_deriv); %  Compute error of approx.
    hvec(i) = h;
    evec(i) = abs_error;
    h = h/2;                            %  Decrease step size h.
  end

  loglog(hvec,evec)
  xlabel('h'), ylabel('abs error(h)')
  title('Divided Difference Approx Error vs h')