Re: Arguments for supporting Motion P1788/0023.01:NoMidRad
Dear John,
you can find many such articles on Jiri Rohn's web page:
http://uivtx.cs.cas.cz/~rohn/
http://uivtx.cs.cas.cz/~rohn/publist/000home.htm
see, e.g.
http://uivtx.cs.cas.cz/~rohn/publist/!handbook.pdf
Prof Rohn uses the notation
x= [x_c - \Delta_x, x_c + \Delta_x]
which is in fact a mid-rad form.
I think he is doing this in order to please
inf-sup readers. The underlying form in most
of his theory and algorithms is the mid-rad one.
Here one can argue that everything can be formulated in
inf-sup form. Similarly Arnold claims that Kaucher arithmetic
can be written in standard form. This is true. One can also
claim that all linear algebra can be fomulated without the
use of vectors and matrices. Which does not imply that
vectors and matrices are useless.
Svetoslav
On 15 Sep 2010 at 7:56, John Pryce wrote:
Subject: Re: Arguments for supporting Motion P1788/0023.01:NoMidRad
From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
Date sent: Wed, 15 Sep 2010 07:56:41 +0100
To: "<stds-1788@xxxxxxxxxxxxxxxxx>" <stds-1788@xxxxxxxxxxxxxxxxx>
> Rudnei, P1788
>
> On 15 Sep 2010, at 01:46, Rudnei Cunha wrote:
> > 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.
>
> Can you point us to just one article where the advantage of a mid-rad type in interval numerical
linear algebra is demonstrated, with algorithm(s) and performance comparisons? Our standard is
about _rigorous_ enclosures, so it must be about those, not approximate ones. And INTLAB's
fast matrix multiplication won't do, because it doesn't use a mid-rad type, only a split into a
"mid" and a "rad" point matrix.
>
> John