Re: [Gretl-devel] fdjac precision question
On Tue, 29 Dec 2015, oleg_komashko(a)ukr.net wrote:
Dear Riccardo, My simple script uses exactly Richardson
extrapolation but it uses a simplistic method for defining the
step. 3 digits better is by far too large. Clearly, fdjac uses a
more advanced way to find h. It looks, as if it has a buglet
inside.
I don't think there's any bug in Jack's Richardson code. In fact I
believe the only reason you're getting more accurate results in this
case is that you got lucky with your "simplistic method" for setting
h. If I just change the code in our minpack-derived fdjac2.c to use
your choice of
h = 1000 * sqrt(DBL_EPSILON)
in place of
h = fabs(x[j]) * sqrt(DBL_EPSILON)
I get a value for sin'(0.1) which is good to 12 decimal places!
I don't suppose this would be consistent across arbitrary functions,
but it may be worth experimenting with a bigger h, or a different
formula for h, in the "quality = 2" case.
Allin