Re: Motion 6
On 2009-09-21 10:43:48 +0200, Arnold Neumaier wrote:
> Vincent Lefevre wrote:
> >On 2009-09-17 12:51:11 +0200, Arnold Neumaier wrote:
> >>For rigorous multiple precision calculations, a triplex representation
> >>is far superior in this respect, as - unlike a midrad representation -
> >>it degrades gracefully when the interval gets wide, and allows the
> >>representation of intervals like [1,inf], which the midrad
> >>representation doesn't.
> >
> >This is slower.
>
> This is not much slower, since the multiprecision part takes the
> bulk of the computation time.
True, but this is a bit useless. If intervals can get wide, it would
be better to use infsup for such kind of applications.
> >So I wouldn't say it is superior. In some applications
> >(probably in particular those that are best with midrad), degrading
> >gracefully is not necessarily useful. For instance, when the error no
> >longer remains small, the results could be regarded as meaningless,
> >and recomputing the results with more precision may be necessary.
>
> There is no clear marhgin when something becomes meaningless;
> see the example from my previous mail
> x in 1e-10000 + [0,Inf], which encodes sign information,
>
> This makes it important to have graceful degradation.
With midrad typical intervals, the error is small, so that the
interval keeps the sign information, unless the real value is 0.
This is the only case where the triplex representation can be
better. Then the question is whether such a case occurs often
enough in practice.
Anyway standardizing either midrad or triplex (or both) in addition
to infsup would be better than requiring infsup alone.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)