function F = NewtonDividedDifference2(x,f,df)
%
% This function implements Newton's Divided Difference Algorithm
% for Hermite Interpolation. F is the vector of coefficients
%
% Written by Ming Gu for Math 128A, Fall 2008
%
n = length(x);
z = kron(x(:),ones(2,1));
P = diag(kron(f(:),ones(2,1)));
for k=2:2*n
   j = k - 1;
   if (mod(k,2)== 0)
       P(k,j) = df(k/2);
   else
       P(k,j) = (P(k,j+1)-P(k-1,j))/(z(k)-z(j));
   end
   for j = k-2:-1:1
       P(k,j) = (P(k,j+1)-P(k-1,j))/(z(k)-z(j));
   end
end
F = P(:,1);