On Wed, Jan 03, 2007 at 02:36:14PM -0800, Richard Fateman wrote:
>
>
> > -----Original Message-----
> > From: Robert Dodier [mailto:robert.dodier at gmail.com]
> .....
> > Bigfloat arithmetic isn't much of an
> > issue in numerical integration anyway; integration errors are
> > typically several orders of magnitude larger than the floating point
> > epsilon.
>
> I don't understand this. Bigfloat integration can get higher accuracy if
> you carry more precision and adapt the algorithm. If you want to get a
> value to 50 decimal places, what choice do you have?
I think he meant that typically the error in an estimate of an
integral computed using double precision is dominated by the
truncation error inherent in the method rather than by the
roundoff. So for a method designed for doubles, using bigfloat doesn't
add anything much.
I think most people using numerical integration are generally happy to
have a double precision float's worth of accurate digits.
Perhaps improving the documentation on quadpack, standardizing the
interface with respect to multiple integrals, or creating a special
multiple integral routine would be a better time investment.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan