Re: Motion P1788.1/M001.02 -- YES
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.
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
>
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v2.0.22 (GNU/Linux)
>
> iQEcBAEBAgAGBQJWZgfIAAoJEIyjRWvAvCeCqb0H/AmwPESMl0y9J4NGN1IH+jMi
> OTzdnKiZmdBLdSwZtOgXs3rmGv/8obz2BXwDnsmA6eg7cJxvSv7rrLel2SICoxoj
> PsAoMBMM5TJKiYMAO0j6+FvVKD2Ke39PpjWqTMO6YtcdS5X2y93rOGzIiAu4rL2o
> STHtJFLo4GDS+4rnEgTyjhlBEIK8dYPvkEdBTiWdrQUlcO6zQu6KuuEoAwB2JtfN
> NKwfy+pr7xRWfHN4N9PyHB7TjrqMBcHrjIr5a2M2rflF9fbkuJ5IASAcD+8REjrD
> mBIW58BB2XbD+pod5M7vRhA989CPCtJHXqaT/KlYsjmEr902ARCoOiN8zYYsifo=
> =8MzP
> -----END PGP SIGNATURE-----
Prof. Svetoslav Markov, DSci, PhD,
Dept. "Math Modelling & Num Analysis", phone: +359-2-979-2876
Inst. of Mathematics and Informatics, fax: +359-2-971-3649
Bulgarian Academy of Sciences, e-mail: smarkov@xxxxxxxxxx
"Acad. G. Bonchev" st., block 8,
BG-1113 Sofia, BULGARIA mobile (gsm): 08888 24567
URL: http://www.math.bas.bg/~bio/
URL: http://www.biomath.bg/S_Markov.php
www.biomath.bg/2016/
http://www.biomathforum.org/biomath/