Re: Arguments for supporting Motion P1788/0023.01:NoMidRad
Yes, absolutely true. Just one typical
example, showing that in linear algebra
the mid-rad form is the natural presentation.
Write the two intervals A, B in mid-rad
form, then write down the condition that
the intersection of A and B is not empty and
you obtain the the basic relation used in Prager-
Oettli theorem. Many of the papers by Jiri Rohn
are actually formulated in mid-rad form.
Svetoslav
On 14 Sep 2010 at 21:46, Rudnei Cunha wrote:
From: Rudnei Cunha <rudnei.cunha@xxxxxxxxx>
Date sent: Tue, 14 Sep 2010 21:46:36 -0300
Subject: Re: Arguments for supporting Motion P1788/0023.01:NoMidRad
To: stds-1788@xxxxxxxxxxxxxxxxx
>
> I strongly agree with Nate. I've seen enough evidence in the field of numerical
> linear algebra using interval arithmetic - both standard and mid-rad
> representations - that have convinced me that, in this field at least, mid-rad
> is the best choice. Leaving it as a sort of "outcast interval arithmetic" would
> not be wise for the scientific community, specially considering that numerical
> linear algebra is at the core of large-scale scientific applications.
>
> Rudnei
>
> 2010/9/14 Nate Hayes <nh@xxxxxxxxxxxxxxxxx>
> Dan Zuras wrote:
> Date: Tue, 14 Sep 2010 22:41:10 +0200
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: rbk@xxxxxxxxxxxxx, 1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Arguments for supporting Motion P1788/0023.01:NoMidRad
>
> Ralph Baker Kearfott wrote:
> >
> > The motion has been put forward by Arnold Neumaier (through Dan Zuras),
>
> I didn't forward the motion. I only suggested a wording for this motion,
> which was put forward by Dan Zuras.
>
>
> > and has
> > been seconded by Nate Hayes. The discussion period therefore begins,
> > and will
> > continue until after the end of Tuesday, October 5.
> >
> > Juergen: Please post this information on the web page.
> >
> > William: Please record this in the minutes.
> >
> > The motion is as follows:
> > ----------------------------------------------------
> >
> > The standard shall not support a midrad interval format or
> > nonstandard intervals, beyond providing conversion support,
> > approximately to the extent specified in the Vienna Proposal.
> >
> > ----------------------------------------------------
> >
>
> . . .
>
> It appears both here & in a private email that Arnold
> really means to bind us rather than the user here.
>
> It is his interpretation that "The standard shall not
> support midrad..." means "The 1788 standards committee
> shall not support midrad...".
>
> ...
>
> I cannot think of any further textual change to the
> motion that embodies this. Let that be the intended
> interpretation for the motion as it stands.
>
> I accept that as a 'friendly interpretation'.
>
> Comments, anyone?
>
> After listenting to the exchanges the past two days, this is also my
conclusion
> of Arnold's position, i.e., he does not oppose that users and
implementers
> should use mid-rad or Kaucher arithmetic, just that these aspects of
interval
> arithmetic should not be supported or endorsed by P1788.
>
> If enough people in P1788 feel so strongly about this as does Arnold and
wish
> to prohibit mid-rad or Kaucher arithmetic, this is fine with me and I
would
> continue to help build such a standard.
>
> However, what is NOT fine with me is that P1788 should then continue
under the
> pretense that it is creating a standard for "interval arithmetic."
Clearly mid-
> rad and Kaucher arithmetic are "interval arithmetic," and no amount of
brow-
> beating will change this fact.
>
> So in that case, the name of the standard and of this working group
should
> change if this motion passes.
>
> Of course, I do not agree with Arnold's views and positions on mid-rad
and
> Kaucher arithmetic. In particular, his assertion:
>
> "1.4. No strong case has been made that ... nonstandard arithmetic
> is actually more efficient on a significant class of problems than what
> can be done without it."
>
> Perhaps he does not care about industries such as CAD, CAM, computer
graphics,
> etc. where fast processing of polynomial b-splines and NURBS is essential
> foundation of almost all computations. But these do represent global,
multi-
> billion dollar industries and with the proper hardware support the
Kaucher
> arithmetic will always be faster than a processor supporting only
textbook
> intervals as he advocates. This subject has already been examined and
discussed
> at length in this forum and also in the position papers Arnold mentions;
so I
> will refer to those rather than taking time to repeat an elaboration of
this
> topic again.
>
> Sincerely,
>
> Nate Hayes
>