RE: Motion 52: final "Expressions" text for vote
The goal of interval computations is to provide enclosures for ranges of functions of real variables over intervals. Interpretation of expressions should be left to the implementation, it is not a question of mathematcial foundations.
It is a question of mathematical foundations of what is the range of x-x when x is in [1,2]. Clearly, the range is 0. It is a question of implementation whether X-X, where X is an interval, would return [0,0] or a wider interval -- as long as what it returns is an enclosure for the exact range.
It would be great if we could always return the exact range, but since the problem of computing the exact range is NP-hard, we will inevitably sometimes produce the enclosure with excess width.
________________________________________
From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] on behalf of G. William (Bill) Walster [bill@xxxxxxxxxxx]
Sent: Saturday, November 23, 2013 3:07 PM
To: Ned Nedialkov; Dan Zuras Intervals
Cc: stds-1788@xxxxxxxxxxxxxxxxx
Subject: Re: Motion 52: final "Expressions" text for vote
Thanks, Ned.
Yes, the documentation
<http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDUQjBAwAQ&url=http%3A%2F%2Fwww.ti3.tuhh.de%2Fkeil%2Fprofil1%2Fdocu%2FProfil.texinfo_toc.html&ei=FSCRUs33JsKEjALs14HwCA&usg=AFQjCNGF48QkeunnGnzQcpInGM0Ouyh_JA&bvm=bv.56988011,d.cGE>
for FILIB++ is a step in the right direction, but it and the references
therein remain incomplete. For example, what is the containment set of
1 / ( 1 / [1, +oo] ) ?
In addition, with the interval variable X = [1, +oo], under what
conditions are [1,1] and [0,0] the containment sets of
1 / (1 / X)
and
X - X,
respectively?
It seems to me that a complete mathematical foundation for computing
with intervals must define containment sets for these and many more
expressions and functions.
I did not see any mathematical foundation in the the PROFIL/BIAS
documentation in
<http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CDUQjBAwAQ&url=http%3A%2F%2Fwww.ti3.tuhh.de%2Fkeil%2Fprofil1%2Fdocu%2FProfil.texinfo_toc.html&ei=FSCRUs33JsKEjALs14HwCA&usg=AFQjCNGF48QkeunnGnzQcpInGM0Ouyh_JA&bvm=bv.56988011,d.cGE>
Cheers,
Bill
On 11/23/13 11:03 AM, Ned Nedialkov wrote:
> On 2013-11-23, at 1:24 PM, Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx> wrote:
>> Bill,
>>
>> Have their not been publications over the years of various
>> ways to implement intervals? Can we not pick from one of them
>> as a basis for our standard. And I say 'basis' because there
>> are clearly other things people would like in their standard.
>>
>> Yours,
>>
>> Dan Zuras
>
> FILIB++ and PROFIL/BIAS are pretty good. There is also Gaol, which I do not know very
> well.
>
> Ned
>
>
>