natural interval extension
Dear Frederic,
I agree. We do not need to redefine the term
"natural interval extension", we can just avoid using it.
Moreover, what seems natural for someone, may not
seem natural for someone else.
Redards, Svetoslav
On 8 Dec 2015 at 9:18, Frederic GOUALARD wrote:
Date sent: Tue, 08 Dec 2015 09:18:05 +0100
From: Frederic GOUALARD <Frederic.Goualard@xxxxxxxxxxxxxx>
To: Svetoslav Markov <smarkov@xxxxxxxxxx>
Copies to: Michel Hack <mhack@xxxxxxx>, stds-1788
<stds-1788@xxxxxxxxxxxxxxxxx>,
stds-1788@xxxxxxxx
Subject: Re: Motion P1788.1/M001.02 -- YES
Organization: UFR SCIENCES ET TECH/DEPT. INFORMATIQUE
> Dear Svetoslav,
>
> Le 2015-12-08 08:21, Svetoslav Markov a 'ecrit :
> > The term "natural interval extension" meaning replacement
> > of all real quantities and operators by interval
> > ones has been introduced by Moore.
> >
> > So I find great the suggestion by Michel to rename this
> > term "Moore Interval Extension" in tribute to R Moore.
>
>
> Giving a new, additional, name to an existing procedure is one thing
> (and Michel's suggestion is a great one). Redefining a term whose use is
> already pervasive in the interval literature with a new meaning is a
> horse of a completely different color.
>
> If we had to name in the standard what has often been called "natural
> interval extension" so far, I would applaud Michel's suggestion to use
> "Moore Interval Extension".
>
> I have strong reservations to redefining "natural interval extension" to
> something entirely different, even if proposing in parallel a new name
> for the old procedure. That is calling for a great deal of confusion in
> the future.
>
> Best regards,
>
> FG.
>
>
> >
> > Svetoslav
> >
> >
> >
> >
> > On 7 Dec 2015 at 23:27, Fr'ed'eric Goualard wrote:
> >
> > Subject: Re: Motion P1788.1/M001.02 -- YES
> > To: Michel Hack <mhack@xxxxxxx>, stds-1788
> > <stds-1788@xxxxxxxxxxxxxxxxx>
> > From: Fr~A©d~A©ric Goualard
> > <Frederic.Goualard@xxxxxxxxxxxxxx>
> > Date sent: Mon, 7 Dec 2015 23:27:20 +0100
> >
> >> -----BEGIN PGP SIGNED MESSAGE-----
> >> Hash: SHA1
> >>
> >> Dear Michel,
> >>
> >> On 12/07/2015 10:08 PM, Michel Hack wrote:
> >> > I vote YES to the text of Clause 4 of Nov 30, 2015.
> >> >
> >> > As for "Natural Interval Extension" -- it seems to me that this is
> >> > the proper term. Is is also consistent with the parent standard
> >> > 1788-2015.
> >> >
> >> > Now, there may indeed be confusion if others have used this term
> >> > to denote what I might call "Moore Interval Extension".
> >> >
> >> > So I would suggest, as an editorial comment, that we add the
> >> > following at the end of Clause 4.4.4:
> >> >
> >> > The term "Natural Interval Extension" has frequently been used to
> >> > denote the result of expression evaluation, as opposed to the hull
> >> > of the range. The term "Moore Interval Extension" might have been
> >> > more appropriate for this.
> >> >
> >> > Michel.
> >> >
> >> > P.S. The Wikipedia article does not define the "function rule"
> >> > that it applies to its definition of "natural interval extension".
> >> > The problem of course is that many expressions can be used to
> >> > compute a function, and some functions might not even use an
> >> > expression -- they might use table-based interpolation for
> >> > example. So while there may be a "natural interval expression
> >> > extension", the notion does not make sense for a *function*.
> >> >
> >> > An article by Alexandre Goldsztein uses "Natural A-E extension"
> >> > which however restrics the expression to single-use variables.
> >> > ---Sent: 2015-12-07 21:33:52 UTC
> >> >
> >>
> >> Two months ago, I searched my library for a definition of "Natural
> >> interval extension". Here is what I found:
> >>
> >> Introduction to Interval Analysis, Ramon Moore, R. Baker Kearfott and
> >> Michael J. Cloud. SIAM 2009.
> >> The authors define "natural interval extension" on Page 47 in an
> >> informal manner (replace all real quantities and operators by interval
> >> ones) that corresponds to my own understanding.
> >>
> >> Applied Interval Analysis. Luc Jaulin, Michel Kieffer, Olivier Didrit
> >> and Eric Walter. Springer 2001.
> >> The authors define a "natural inclusion function" on Page 30, again by
> >> mapping real quantities to interval ones. Still rather informal.
> >>
> >> Validated Numerics. Warwick Tucker. Princeton University Press 2011.
> >> Warwick defines a "natural interval extension" informally as
> >> substitution from real objects to interval ones.
> >>
> >> I could not find the expression in "Interval Methods for Systems of
> >> Equations" by Arnold Neumaier. However, I surmise he would sanction
> >> the syntactical definition, as it is the one used in a paper he
> >> coauthored with Daney and Papegay:
> >> Interval Methods for Certification of the Kinematic Calibration of
> >> Parallel Robots. D. Daney, Y. Papegay, and A. Neumaier. Proceedings of
> >> the 2004 IEEE International Conference on Robotics & Automation.
> >>
> >> I believe there is enough papers and books that do not use "natural
> >> interval extension" in the sense used in P1788.1 to make its
> >> (re-)definition there objectionable.
> >>
> >> Best regards,
> >>
> >> FG.
> >> - --
> >> Fr'ed'eric Goualard LINA - UMR CNRS
> >> 6241
> >> Tel.: +33 2 76 64 50 12 Univ. of Nantes - Ecole des Mines de Nantes
> >> 2, rue de la Houssini`ere - BP
> >> 92208
> >> http://frederic.goualard.net/ F-44322 NANTES CEDEX 3
> >>