Re: [Bug-gsl] GSL interpolation

[Evgeny Kurbatov]

On Thu, 26 Jul 2012 14:39:21 -0400
Jens Chluba <address@hidden> wrote:

> Hi there,
> 
> just a comment on the new convention for interpolation. Round-off
> error lead to problems with
> 
>   if (x < interp->xmin || x > interp->xmax)
>     {
>       GSL_ERROR_VAL("interpolation error", GSL_EDOM, GSL_NAN);
>     }
> 
> if indeed x very close to the boundaries but within the interval
> [xmin, xmax]. It is probably better to put something like
> 
>   if (x < interp->xmin*(1.0-1.0e-14) || x >
> interp->xmax*(1.0+1.0e-14)) {
>       GSL_ERROR_VAL("interpolation error", GSL_EDOM, GSL_NAN);
>     }
> 
> This allows for a tiny range of extrapolation but fixes the round-off
> error problem.

Hi, Jens!

I was the one who proposed a patch for interpolation routines
toughening control to the boundary violation. There was times when I
was sorry about that, but now the belief rises that this was right. The
control forces you to think deeper and be more accurate.
So hold on, be man!

> 
> In addition, I was wondering if the GSL team could be interested in
> some pretty fast and accurate integration schemes based on the
> Patterson quadrature rules? These are fully nested and converge very
> rapidly. I have the required c++ code and will be happy to provide
> them. Certainly, this can only be a base for GSL, since you guys have
> much higher coding standards...

I don't mind.

Best witches,
Evgeny Kurbatov