Re: A simple interval challenge
Jean-Pierre Merlet schrieb:
I think that there is a flaw in this test or at least that the results
should be divided into 2 categories:
1- results provided by interval experts that will spend some time
re-arranging expressions for this particular case to get the "best" result
2- results provided by general purpose interval software (the one that
the end-user will use because they don't have the knowledge to do
otherwise). In that case the data should be provided "as it" because the
system and bound may be the result of some other calculation and are not
known in advance.
This is a misunderstanding.
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.
Category 2 amounts to using a package that does range bounding using
branch and bound, which will yield very accurate ranges but at much
higher costs, not tolerable when the enclosure is needed millions of
time.
So this contest is not about testing the performance of existing
software but about testing (and making public) the bag of tricks
experts have to squeeze the best out of a very limited budget for
one range enclosure.
I am not interested in enclosures that need more than 200 effective
interval operations; this probably eliminates most branch and bound
packages (quite apart from the fact that it is difficult to count
there the number of operations).
The results by Mihaly Markot were mentioned only in order to help
people understand the nature of the problem, since they give
accurate values for the width of the range, and since they show
where the worst cases are attained. In particular, they show that
pure monotonicity arguments cannot give the exact range.
Arnold Neumaier