Re: MidRad -- and Two Different Application Domains (TDAD).
On 2009-09-21 06:21:51 +0200, Hossam A. H. Fahmy wrote:
> > > lack of representation for semi-infinite intervals);
> >
> > This one is not a difficulty. On the contrary, it is simpler: as
> > soon as the error bound becomes infinite, return R.
> >
> On this, however, I disagree with Vincent. What you say is correct for the
> first domain described by Michel at the start of this thread
>
> "One domain of application is operating with uncertain numbers, where an
> interval represents a single numeric value with bounded uncertainty.
> In this domain MidRad and InfSup are logically interchangeable"
>
> but not for the second domain
>
> "A totally different domain is that of intervals representing ranges of
> different, individually-precise, numeric values, where that range may
> be unbounded on one or both sides. InfSup is the only flavour that
> can handle this domain, and semibounded intervals can only be converted
> to totally-unbounded MidRad from, i.e. Entire."
>
> Michel made a very important observation by separating those two domains.
I don't think we disagree here. I've said elsewhere that if the error
can become large (this is typically the case with the second domain),
the user should *not* use midrad. What I was saying above is that it
is still possible to *specify* midrad in such degenerate cases, e.g.
by returning R.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)