To symmetrize the resulting matrix , whose columns are the vectors , , from (45) the matrix

is constructed.

With exact arithmetic, discrete Newton methods converge quadratically
if each goes to zero as does [16].
However, the roundoff error limits the smallest feasible size of difference
interval in practice and, hence, the accuracy (a combination of roundoff and
truncation errors) that can be obtained. As the gradient becomes very
small, considerable loss of accuracy may also result from *
cancellation*
errors in the numerator
(a large relative error, , from the subtraction of two
quantities, **s** and , of similar magnitude).
Consequently, discrete Newton
methods are inappropriate for large-scale problems unless the Hessian
has a known sparsity structure
and this structure is exploited in the
differencing scheme.