Re: semantic theorems of modal interval analysis
The original modal intervals theory presents gaps in its mathematical
constructions as well in some critical proofs. You can find a
reformulation based only on Kaucher intervals as well as new proofs
and some new developments in the following manuscripts:
http://hal.archives-ouvertes.fr/hal-00294219/en/
http://hal.archives-ouvertes.fr/hal-00294222/en/
An informal presentation of the new formulation is also proposed in
http://www.goldsztejn.com/publications/QCP2005.Goldsztejn-Daney-Rueher-Taillibert.pdf
Alexandre
On Tue, Jun 5, 2012 at 11:35 AM, Arnold Neumaier
<Arnold.Neumaier@xxxxxxxxxxxx> wrote:
> On 06/05/2012 11:26 AM, John Pryce wrote
> [Re: Motion M0034.01 -- Notations}:
>>
>>
>> On 4 Jun 2012, at 15:14, Nate Hayes wrote:
>>
>>> The semantic theorems of modal interval analysis generalize the
>>> Fundamental
>>> Theorem of Interval Arithmetic ...
>>
>>
>> Nate, is there ANYWHERE that proofs of these theorems are available? Can
>> we put them on our web site? Or are they jealously guarded by the Gardenes
>> group? I've asked before.
>
>
> What is rigorously known about the semantics of modal interval arithmetic is
> summarized in my manuscript
> Computer graphics, linear interpolation, and nonstandard intervals
> http://www.mat.univie.ac.at/~neum/ms/nonstandard.pdf
>
>
> Arnold Neumaier
--
Dr. Alexandre Goldsztejn
CNRS - Laboratoire d'Informatique de Nantes Atlantique
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