In a quasi-Newton method, such as that due to Davidon, Fletcher and Powell or Broyden Fletcher Goldfarb Shanno ( BFGS method ) an estimate of the full Hessian, \ frac { \ partial ^ 2 S } { \ partial \ beta _ j \ partial \ beta _ k }, is built up numerically using first derivatives \ frac { \ partial r _ i } { \ partial \ beta _ j } only so that after " n " refinement cycles the method closely approximates to Newton's method in performance.
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