On 1/3/07, Richard Fateman <fateman at cs.berkeley.edu> wrote:
> Any method designed specifically and only for doubles would be inappropriate
> for bigfloats. There are methods that can be used for variable precision,
> adjusting their convergence criteria based on the requested accuracy and
> perhaps the precision of basic arithmetic. These generally produce
> increasing accuracy for high precision (and more time, subdivisions, etc.).
> They also sometimes find answers where lower precision does not converge at
> all.
Well, there aren't any constant values appearing in the Romberg
method so, if you're willing to wait and the integrand in question isn't too
badly behaved (a vague attribute, I know), you should be able to get any
precision you want. From looking at the bromberg code and trying an
example, I believe that is indeed the case. So that is a capability which
is not available otherwise. On reconsideration I guess we should keep
bromberg.
Robert