Evaluating extremes in a closed interval



Daniel Lakeland wrote:
> 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.

This would be the mathematical solution for the problem, using 
real numbers.

A fixedpoint solution itself will produce additional errors, that 
are missing in such an approximation model. To add them, leads to 
the same kind of problem, I'm currently investigating: error 
functions like beds of nail.

Using fixedpoint (which means integers to be devided by a factor 
at the end and balancing subexpressions to avoid destortions) is 
much cheaper in terms of computational power and memory, than 
using some float format, if no floatingpoint processor is 
available and if the computational errors are tolerable.

It seems to me, that dew point is a good candidate to get it 
solved: looks complicated in the original formula, but isn't.