Re: YES on Motion P1788/0019.01
> Date: Sun, 12 Sep 2010 21:52:06 +0200
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: YES on Motion P1788/0019.01
>
> Dan Zuras Intervals wrote:
> >> . . .
> >>
>
> > We can go as you please but I prefer to consider the
> > possibility that mid-rad forms have merit.
>
> The merits are such that no one in the last 50 years was moved by
> them to create a serious implementation, although the ideas were around
> as long as those for infsup.
>
> It is very unwise to cater in a standard for possibilities that
> haven't already left a strong trace in the past, and without having
> even a blueprint (position paper) on how such a possibility should
> be fleshed out.
I am moved by some papers on the subject to consider
that we must find a way to make mid-rads both efficient
& well characterized.
In particular, interval methods have a tendency to turn
floating-point tasks into combinatorial tasks. Thus,
one sometimes has to look at exponentially many endpoints
to find a tightest enclosure.
There are linear algebra problems for which Jacobian
methods exist that circumvent this problem. At least to
a good approximation & only for the mid-rad forms.
This means that some problems which are NP-hard for
inf-sup forms are polynomial for mid-rad forms.
It is this that gives merit to mid-rads for me.
It is this that makes me believe that we have to find
a way to include them without watering down the
specifications for inf-sup forms.
>
>
> > Just how
> > we are to restrict their behavior in any meaningful
> > way is the subject of some future motion written by
> > those who know this subject far better than I.
> >
> > Let's see what they come up with rather than assume
> > their failure from the beginning.
>
> Motion 16 required infsup and allowed midrad as additional type.
> It was proposed by you and found a majority.
> Passed motions should not be undone without _very_ strong reasons
> for doing so.
>
> Why did you change your mind?
>
>
> It is much better to stay with motion 16 until those who know
> this subject far better than you have come up with some convincing
> details on how we are to define midrad-only behavior in a way that among
> other things, in particular (i) and (ii) are catered for.
>
> If a strong proposal along these lines is made (which I consider very
> unlikely), it is still possible to relax Motion 16 at that time.
>
> But it is irrational to do it without having evidence that it would be
> an improvement of the standard-to-be.
>
>
> Arnold Neumaier
Ah, so it is your position that the standard should
eliminate the mid-rad forms altogether in favor of
the inf-sup forms.
Then make a motion to that effect. I will second it.
It is a defensible position. It would greatly
simplify our standards work to only have to deal with
the inf-sups from now on. And much that is
controversial about our current approach would have
easy & obvious solutions.
But don't go into it thinking that we will not pay
a price for such a simplification. We will.
Dan