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Calculates an approximation to the Newton-Raphson search direction using past gradients to build a serviceable substitute to a Hessian. The Hessian matrix is never explicitly formed or inverted. This function is the implementation from section 4 of




   dx_hist         - history of x increments,
                     bookshelf array

   dg_hist         - history of gradient increments,
                     bookshelf array

   g               - current gradient

   n_grads         - max number of past gradients to 
                     use for the Hessian estimate


   direction       - LBFGS approximation to the 
                     search direction


The L-BFGS algorithm is the default of fminnewton.m, and is a good mix of computational efficiency and fast convergence.

See also

fminnewton.m, hessreg.m, linesearch.m

Version 2.2, authors: Ilya Kuprov, David Goodwin