Please clarify Re: The current proposal
Siegfried et al,
Please excuse my possible obtuseness. However, it is
unclear to me precisely what the "current proposal for
interval arithmetic" to which you refer is. Can you
help us by stating specifically to what paragraph and
to what document you are referring? Are you referring
to the latest "Vienna proposal?" Are you referring
to part of the email discussion?
Baker
P.S. Viewing our progress in formalizing a working
document, I see that we are almost finished with
agreeing on procedure. Once we have that, we
can start making solid decisions on specific issues.
I think, however, that it must be clear what we
are talking about, and we should consider such
issues one by one, to the extent that it is
possible.
On 2/21/2009 8:35 PM, Siegfried M. Rump wrote:
> Dear all,
>
> we are discussing the standardization of interval arithmetic. This
> is not intended to pass and put into the cabinet, but intended to use.
>
> May I ask how many of you have experience in using interval arithmetic?
>
> Here is why I must insist that the current proposal is academic and
> puts burden of case distinctions on the user.
>
> Trust me, it is very natural in interval arithmetic to do interval
> calculations with the bounds.
> For a given function F, for example, X=F(interval(A.sup)) should give an
> inclusion of the value of F at the right bound of A.
>
> With the current proposal, this needs a case distinction:
>
> if A.sup==Inf
> X = F(interval(realmax,Inf));
> else
> X = F(interval(A.sup));
> end
>
> This burden is on the part of the user. Even worse, it is likely to be
> forgotten and to pass unoticed. And then false results may appear, the
> worst what can happen to a verication method.
>
> Let me transpose this to the floating-point world.
>
> Imagine the question "What is the result of -0==0" is at stake. There
> are good arguments that it should be true, like in IEEE 754, but one
> may also argue that these are two different quantities, so how can they
> be equal.
>
> Now suppose it is voted for the latter, so that from now on one cannot
> just write
>
> res = ( x==y );
>
> but must use
>
> if abs(x)==0
> res = ( abs(x)==abs(y) );
> else
> res = ( x==y );
> end
>
> or alike. It may be perfectly documented, but is this reasonable?
>
> IMHO the current proposal for interval arithmetic is very similar.
>
> Best wishes
>
> Siegfried M. Rump
>
>
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R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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