Re: numerical differentiation?

[Brian Gough <bjg at network-theory dot co dot uk>]

Regarding endpoint problems and singularities. In QUADPACK a similar
situation occurs. It is handled by having two versions of the general
integration function (QAG vs QAGP). One version assumes a well-behaved
function which can be evaluated anywhere. The other version avoids
using endpoints (in fact, it avoids a set of user-specified singular
points).

For numerical derivatives it sounds as if you could have a similar
setup.  One routine would be free to evaluate the function
anywhere. Another routine would take a range as an argument and avoid
the endpoints. In this way the routine can choose the type of
derivative to use -- one-sided if the step-size would overshoot the
end, but symmetric in the middle. Since the function will be varying
the stepsize it may need to change its choice dynamically.

Gerard Jungman writes:
 > I don't think we should introduce any new multimin functions. Brian
 > should look at this as well, but I think we can just use the current
 > interfaces. You can wrap the numerical differentiation inside
 > the "df" part of a gsl_function_fdf (or gsl_multimin_function_fdf,
 > whatever... Brian: why do we need gsl_multimin_function_??? as well);

... not sure I understand what the question is hear.