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2.5.2 Discrete Newton

Standard discrete Newton methods require n gradient evaluations and operations to compute and symmetrize every Hessian . Each column i of can be approximated by the vector

where is a suitably chosen interval [30]. This interval must balance the roundoff error, proportional to , by formulation, with the truncation error, proportional to . A simple estimate for a well-scaled problem to balance the two errors is .

(See exercise 6.)