Re: Motion 19.02 NO - distorted arguments
On 1 Nov 2010 at 19:17, Arnold Neumaier wrote:
Date sent: Mon, 01 Nov 2010 19:17:13 +0100
From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
Organization: University of Vienna
To: Svetoslav Markov <smarkov@xxxxxxxxxx>,
1788 <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Re: Motion 19.02 NO
> Svetoslav Markov wrote:
> >
> > My vote to motion 19.02 is "no".
> >
> > I would vote "yes" if either:
> >
> > a) the motion is modified so that an implementation
> > that supports only an implicit type is also conforming
> >
> > b) the name of the interval arithmetic standard is
> > modified accordingly.
> >
> > Svetoslav Markov, IMI-BAS
> >
> > PS. Motion 19.02 makes a significant step towards the
> > recognition of the "mid-rad" implementations as auxiliary to
> > "inf-sup". However, I think that "mid-rad only" arithmetic
> > should also be conforming. Let me recall the two main
> > mathematical arguments against "mid-rad only" support:
> >
> > 1. infinite intervals are not representable in mid-rad, and
> >
> > 2. when the midpoint of a (real) interval is exactly in the middle
> > between two machine numbers, then mid-rad presentation is not unique.
> >
> > I do not find these arguments sufficiently serious.
>
> You grossly distort the argumentation against a mid-rad datatype.
>
> The main argument against it is that there has been _extremely_ little
> past use of mid-rad arithmetic on single intervals. (The only serious
> use of mid-rad is for vectorized matrix-vector and matrix-matrix
> multiply, and this application doesn't make use of a mid-rad interval
> format, but does all computations by means of a midpoint matrix and a
> radius matrix. So a standard on midrad intwervals would have no bearing
> on this.
>
I said _mathematical_arguments_ .
I tried to summarize the main _mathematical_arguments_ against mid-rad.
I agree that there has not been too many applications related to mid-rad.
But I do not think that such arguments are of _mathematical_ nature.
Do I distort any _mathematical_ arguments?.
Svetoslav