[std-interval] More on interval computations as proofs

[R. Baker Kearfott]

Certainly, it is desirable that sqr(x) return [0,1] for x=[-1,1]. 
However, isn't the question of x*x returning [0,1] instead of [-1,1]
a question of optimization, and of proper interpretation of what
the programmer intended?  Also, have we distinguished what should
be mandated in the standard and what is just desirable in an
implementation?

Baker

At 05:55 AM 10/6/2006 +0200, Guillaume Melquiond wrote:
>Le jeudi 05 octobre 2006 à 22:42 +0200, Gabriel Dos Reis a écrit :
>> Guillaume Melquiond <guillaume.melquiond at ens-lyon.fr> writes:
>> 
>> [...]
>> 
>> | So, to qualify your point on straightforward translation, I would say
>> | that you are right for resolution algorithms (finding roots, solving
>> | differential equations, and so on), as they simply won't work. But for
>> | evaluation functions, you don't have to rewrite them.
>> 
>> so, are you suggesting that basically x +-> x * x should return [-1,
>> 1] on [-1,1], instead of [0, 1]? (I though a simple function to keep
>> the question simple).
>
>I am obviously not saying that x*x "should" return [-1,1]. I'm just
>saying that, if it returns [-1,1] instead of [0,1], that doesn't matter
>for solving things. Rewriting an evaluation function to take into
>account interval decorrelation will improve the performance of solvers a
>bit (a few iterations less), but it generally won't have any influence
>on the quality of the results.
>
>Best regards,
>
>Guillaume
>
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R. Baker Kearfott,    rbk at louisiana.edu   (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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