Re: Solve exact problem with approx solution, or solve approx problem with exact solution

"Schoenfeld" <schoenfeld1@xxxxxxxxx> wrote in message
news:1147676627.082933.272060@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

In my experience, I cannot decide between the two. The 'most important'
or 'most fundamental' choice depends on the areas of mathematics you
are working in. If you are messing around in number theory, the exact
symbolic solution is usually _the only solution_ that matters (i.e.
"what looks nicest is better"). You can approximate an exact symbolic
solution so many other ways and the symbolisms can be, seamingly,
_irreconcilable_.


However, if you are dealing in computational mathematics, things like
Neural networks, self-organizing maps, cellular automata, then accurate
but computationally simpler approximations seem to be more fundamenta
(i.e the least complex algorithms)

Good topic.

As a practicing engineer, I consider myself a mathemetician on occassion.
Math is purely a means to my end, which is to obtain a solution to the
problem at hand. I do attempt symbolic solutions, but these solutions are
almost always the answer to a simplified version of the problem. Symbolic
partial solutions are helpful to verify the full computational solution is
in the right neighborhood, but usually not much more. I would put
computational vs. symbolic results at a 20:1 ratio for my work. I do prefer
the computational approach.


.