[std-interval] More on interval computations as proofs

[Guillaume Melquiond]

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