Re: back to the roots

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

Ahhh, but the real question is whether the exact dot product is 
necessary to compute results required to develop sharp and fast interval 
library routines that enclose the containment set of a given function 
over a given non-degenerate interval argument.  I do not know of any.  
Do you have examples?

Cheers,

Bill



On 6/29/13 9:48 AM, "Neher, Markus (IANM) [IANM ist die 
Organisationseinheit Institut für Angewandte und Numerische Mathematik 
am KIT]" wrote:
> Bill,
>
> > 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. 
>
> Hypothetical question: If practical input arguments are only accurate 
> to 4 decimal digits, then why bother to compute function values to 
> high precision of low accuracy?
>
> One reason is that even though data may be known to be inaccurate, 
> computations are nevertheless performed with floating point numbers. I 
> think that keeping the influence of roundoff errors as small as 
> possible is not only of academic interest, but also a practical 
> concern. Accurate elementary functions are one means to achieve this, 
> and so is an exact dot product.
>
> Regards,
>
> Markus