Re: back to the roots
Many problems end up in solving some linear system. Ulrich Kulisch has
already pointed out how solving linear systems benefits from an EDP.
Regards,
Markus
On 06/30/2013 04:54 AM, G. William (Bill) Walster wrote:
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