(UTC) 

 :: I don't understand what this business is with inverting the Hessian.  Why would you ever invert the Hessian when you can just rearrange the problem to be solved as a traditional linear system?  eg, H(f)*(Xn+1 - Xn) = Grad(f).  Then you can just solve for (Xn+1 - Xn) using, say, Gaussian elimination, and add that to the previous Xn.   20:44, 15 February 2009