On Wed, Apr 18, 2007 at 09:23:11PM +0200, Albrecht Frenzel wrote:
> Thanks for your answers.
>
> I want to investigate the effect of using a fixedpoint
> approximation TD for the function Td, using a selectable
> precision. Td describes the dependency of the dew point from
> temperature and relative humidity of air.
....
This sounds like a very interesting problem. I think, if I can restate
it, that you're looking for a way to approximate a certain function
using only integer arithmetic and compute the maximum error bound due
to the discrete arithmetic.
I'm wondering if there isn't a way to change the way the problem is
posed so that you can get a better result. Of course the original
function is very smooth. Perhaps you can store the value of the
function, and the gradient of the function at a set of regularly
spaced grid points (that would be 3 numbers for each grid point, one
for the function and two for the components of the gradient), and then
you evaluate the function by finding the closest grid point, and using
linear extrapolation with the gradient you refine the computation. You
could pre-compute the maximum error bounds for such a computation
using maxima using calculus methods rather than numerical methods.
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan