nag_numdiff_1d_real_absci (d04bbc) generates abscissae about a target abscissa
for use in a subsequent call to nag_numdiff_1d_real_eval (d04bac)
nag_numdiff_1d_real_absci (d04bbc) may be used to generate the necessary abscissae about a target abscissa
for the calculation of derivatives using nag_numdiff_1d_real_eval (d04bac)
For a given
, the abscissae correspond to the set
points will be returned in ascending order in xval
. In particular,
will be equal to
Lyness J N and Moler C B (1969) Generalised Romberg methods for integrals of derivatives Numer. Math. 14 1–14
nag_numdiff_1d_real_absci (d04bbc) is not threaded in any implementation.
The results computed by nag_numdiff_1d_real_eval (d04bac)
depend very critically on the choice of the user-supplied step length
. The overall accuracy is diminished as
becomes small (because of the effect of round-off error) and as
becomes large (because the discretization error also becomes large). If the process of calculating derivatives is repeated four or five times with different values of
one can find a reasonably good value. A process in which the value of
is successively halved (or doubled) is usually quite effective. Experience has shown that in cases in which the Taylor series for for the objective function about
has a finite radius of convergence
, the choices of
are not likely to lead to good results. In this case some function values lie outside the circle of convergence.
See Section 10
in nag_numdiff_1d_real_eval (d04bac).