On 1/3/07, Richard Fateman <fateman at cs.berkeley.edu> wrote:
> The Romberg program was a short (1 page) Fortran program that I copied from
> my (graduate) numerical analysis course notes into lisp, in 1969 or so. I
> had no idea that it would last this long in Macsyma/Maxima. On the other
> hand, it should not be replaced by something that is functionally inferior
> in any way.
QUADPACK is functionally superior in the aspects which matter most --
it did not fail on problems which romberg and quanc8 failed on,
and its computed estimate meets the specified error tolerance.
> I consider failure to support recursive calls to be inferior,
> but I don't see why the qq programs, properly packaged would not allow
> recursion too.
You'll need to take this up with Stavros, then. He always says that
argument quoting (which is what allows romberg and quanc8 calls
to be nested) is a bad idea. But if you can convince him that quoting
the integrand in QUADPACK functions is a good idea, I will gladly
modify the QUADPACK code accordingly.
By qq I guess you mean QUADPACK. qq is the package which contains quanc8.
> Furthermore, if the qq programs do not support bigfloats, it seems Romberg
> should stay until they do.
I'm not convinced. I don't want to tell people that they should use a
method known to be inferior. 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.
All the best,
Robert