d04bbf generates abscissae about a target abscissa
for use in a subsequent call to
d04baf.
d04bbf may be used to generate the necessary abscissae about a target abscissa
for the calculation of derivatives using
d04baf.
For a given
and
, the abscissae correspond to the set
, for
. These
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
None.
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
The results computed by
d04baf 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.