Re: [Help-gsl] Origin of 2nd round-off term "dy" in function central_deriv.c

[Brian Gough]

At Fri, 16 Feb 2007 21:00:49 -0500 (EST),
Rene Girard wrote:
> On line 24 of the function "central_deriv.c" we have the following
> line:
> 
> double dy = GSL_MAX(fabs(r3),fabs(r5))* fabs(x)*GSL_DBL_EPSILON
> 
> I understand the rest of the function very well and I am able to
> derive the equation for the optimal stepsize "h_opt" in function
> "gsl_deriv_central.c"; however, I am trying to look for a derivation
> for the expression of "dy". I have look in numerous textbooks on
> numerical analysis, in particular the book of Conte and de Boor
> given as a reference in the GSL Reference Manual. 

Thanks for the email.  I think the dy contribution is trying to
capture the rounding error from terms like x+h which is
O(|x|*DBL_EPSILON), but it looks like there is a factor of 1/h^2
missing.

-- 
Brian Gough