Re: inf-sub vs mid-rad and Motion 16
Dear Michel,
thank you, it seems that I did not express myself well.
I should better say:
"1) symmetric conditions have to be imposed
on inf-sup and mid-rad ;"
I am convinced that no one of the two representations should
be given priority. Implementors should have the right to
decide which one to use.
On level one interval arithmetic is independent on
both presentations. All operations, all relations,
all algebraic stuctures are the same. Interval addition
is associative independently of any presentation.
Multiplication is inclusion isotone. Etc, etc.
Any problem can be solved in both presentations,
I beleive. And (when the standard is ready) it will be
interesting to find out the differences, if any.
Mid-rad seems to be a better presentation for computing with
narrow intervals, while inf-sup is better for computing
with wide intervals. There are probably many other pluses and
minuses. In particular, inf-sup allows presentation of
infinite intervals, which I beleive is important for "wide"
computations, however infinite intervals are of no use for
"tight" computations. In contrast, mid-rad allows very
tight intervals, which are important for control of round-off
errors, and not important for solving problems with
wide input intervals.
There is a nice symmetry between the two presentations.
Each one has some advantages and disadvantages.
That is why both representations should be treated
with equal respect. To no one should be given priority.
This is what I wanted to say.
If the standard provides support for infinite intervals,
it will be reasonable to provide support for narrow
intervals as well. The standard should be equally kind
to both presentations, I think.
Svetoslav
On 27 Jun 2010 at 11:00, Michel Hack wrote:
Date sent: Sun, 27 Jun 2010 11:00:02 -0400
To: stds-1788 <stds-
1788@xxxxxxxxxxxxxxxxx>
From: Michel Hack
<hack@xxxxxxxxxxxxxx>
Subject: inf-sub vs mid-rad and Motion 16
> Svetoslav Markov wrote:
> > My vote would be yes if:
> > 1) no different conditions are imposed on inf-sup and mid-rad ;
>
> Can't do, unless we revise our basic assumptions and drop support for
> semibounded inf-sup intervals.
>
> Let's face it: inf-sup and mid-rad have different application domains
> and different properties. There *is* a large common ground, namely
> reasonably narrow intervals (neither too wide, which only inf-sup handles
> well, nor too narrow, which only mid-rad can represent). I'm thinking of
> basic formats here, not the various triplex forms that can do more.
>
> Motion 16 presents the issue in a manner that permits exploitation of
> that common ground, as INTLAB seems to be doing rather nicely.
>
> Michel.
> ---Sent: 2010-06-27 15:09:41 UTC