Re: back to the roots

["G. William (Bill) Walster" <bill@xxxxxxxxxxx>]

Markus,

No.  Such interval libraries returns a sharp bound on the narrowest 
possible interval that encloses the given function over any given 
non-degenerate interval argument.  It should also do this quickly.  
Narrow width and speed are the two figures of merit that make for a 
quality implementation.  In my opinion, the only *requirement* should be 
containment.

I don't understand your sin example, or its connection to your last 
sentence, with which, by the way, I fully agree. :)

Cheers,

Bill


On 6/29/13 8:13 AM, "Neher, Markus (IANM) [IANM ist die 
Organisationseinheit Institut für Angewandte und Numerische Mathematik 
am KIT]" wrote:
> Bill,
>
> > A practical situation in which I can see infinitely precise inputs is 
> > when developing an interval library routine for evaluating some nasty 
> > function, such as the special functions of mathematical physics, or 
> > even fast and sharp interval library routines for elementary 
> > transcendental functions.
>
> Your previous argument shows that such a library is of purely academic 
> interest.
>
> Let us assume that all data is only accurate to at most 4 decimal 
> digits. The number x :=10010 then represents any value in [10005, 
> 10015), so that sin(x) is only known to lie inside [-1,1]. Any attempt 
> to compute sin(10010) more accurately is "not helpful, and can be 
> dangerous".
>
> Obviously, a practical interval standard could be much simpler that 
> the one under development.
>
> Regards,
>
> Markus