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Re: A simple interval challenge

Stefan Ratschan wrote:


On Thu, 2008-11-27 at 13:25 +0100, Arnold Neumaier wrote:

Intended by me for the contest was only category 1, to demonstrate
how much naive techniques can be improved in particular cases that
frequently occur as part of a bigger application, so that tuning it
for optimal performance (and perhaps even putting it into hardware)
is worthwhile.



I fear I still do not fully understand. If that is your goal, why don't
you just take the exact range (computed by whatever method) and plug it
into the application (or put it into hardware)? That would take ZERO
operations in the application (hardware).


Of course, the box over which the range needs to be enclosed
changes from case to case; only the function is the same.
So one needs an algorithm that applies uniformly over a wide
range of input boxes.

But for the evaluation in a contest, one must provide concrete data.
The box chosen is a fairly difficult case for this function.

Even when a method is fine-tuned to this paricular case, the
computation must provide a proof of enclosure, hence is nontrivial.
It will give insight into what sort of tricks are useful for
creating a more complete routine that works well on all input boxes.

And the same kinds of tricks can be applied or adapted to many other
problems of this kind.

To expose insights and tools are the final objectives in the contest.


Arnold Neumaier