function Apr16()
% Assume n = 9 and set F = [F1(x);F2(x);...;F9(x)]
% Let ek be the kth column of eye(9,9).
% Since the jacobian is tridiagonal this means that
%      F1(x) depends only on x(1) and x(2)
%      F2(x) depends only on x(1) and x(2) and x(3)
%      F3(x) depends only on x(2) and x(3) and x(4)
%      F4(x) depends only on x(3) and x(4) and x(5)
%      F5(x) depends only on x(4) and x(5) and x(6)      
%      F6(x) depends only on x(5) and x(6) and x(7)
%      F7(x) depends only on x(6) and x(7) and x(8)
%      F8(x) depends only on x(7) and x(8) and x(9)
%      F9(x) depends only on x(8) and x(9) 

% Let's look at  v = (F(xc+delta(e1+e4+e7) - F(xc) )/delta 
%
%      v(1) = (F1(xc+delta*e1)-F1(xc))/delta
%      v(2) = (F2(xc+delta*e1)-F2(xc))/delta
%      v(3) = (F3(xc+delta*e4)-F3(xc))/delta      
%      v(4) = (F4(xc+delta*e4)-F4(xc))/delta
%      v(5) = (F5(xc+delta*e4)-F5(xc))/delta
%      v(6) = (F6(xc+delta*e7)-F6(xc))/delta
%      v(7) = (F7(xc+delta*e7)-F7(xc))/delta
%      v(8) = (F8(xc+delta*e8)-F9(xc))/delta
%      v(9) = (F9(xc) - F9(xc)

% Thus, we get approximations to J(:,1), J(:,4), and J(:,7).
% Likewise (F(xc+delta*(e2+e5+e8)-F(xc))/delta gives us approximations to
% J(:,2), J(:,5),and J(:,8).
% Likewise (F(xc+delta*(e3+e6+e9)-F(xc))/delta gives us approximations to
% J(:,3), J(:,6),and J(:,9).
% Overall, four F-evals are required.