Re: IEEE Std.1788, inner operations, MD-RDM-IA, the Laws of Motion

[Mehran Mazandarani <me.mazandarani@xxxxxxxxx>]

Dear John

Thank you for your message.
sorry about the confusion. I was going to bring to your attention that what may happen with the so-called dependency problem in analyzing systems. for example, Investigating stability of dynamical systems in which some parameters are uncertain is very crucial, however that issue distorts results for making a decision.

Oliver, suggests using symbolic computing, but I guess there will be some difficulties in that approach for applying it in future in order to present some other notions in mathematics.

Anyway, all these efforts for standardizing the interval computing are making to use it in practice, and I appreciate your efforts and the others.

Roughly speaking:

Definition. Let A and B be interval numbers. If there is Z=(B-A)+A=B+(0-A+A)=B, then we say there is restoration property corresponding to that operations {-,+} which stand for subtraction and addition, respectively.

Definition. Let A be an interval number. If wid(A+A)<wid(A), then we say that operation {+} - stands for addition. - has the self-reduction property.

About the suggestion for presenting the MD-RDM-IA based on a software, that's good idea, and I agree with you. Once it will be prepared, I will send it to you.

Now, let me ask you some questions. What was the definition of derivative for interval-valued function in the page 7 of your presentation at 16th GAMM-IMACS symposium on Scientic Computing, Computer Arithmetic and Validated Numerics 21{26 September 2014, W urzburg, Germany?

What is the notion of differentiability of interval-valued function?

Is it possible you can present a well-define of the notion?

Regards,

Mehran Mazandarani
Department of Electrical Engineering
Ferdowsi University of Mashhad, Mashhad, Iran.
homepage:http://mehran.mazandarani.fumblog.um.ac.ir/
http://works.bepress.com/mehran_mazandarani
IEEE Member, me.mazandarani@xxxxxxxx

On Tue, Oct 20, 2015 at 12:42 PM, John Pryce <PryceJD1@xxxxxxxxxxxxx> wrote:

Dear Mehran

On 19 Oct 2015, at 21:55, Mehran Mazandarani <me.mazandarani@xxxxxxxxx> wrote:
> In the new presentation, the file IC-3.mp4 , the three approaches, IEEE Std.1788 2015, Inner operations, and Multidimensional RDM interval arithmetic are examined by the laws of motion.

As a skeptical (and probably obstinate) mathematician, I still feel you are not clear enough about concepts, so you are confusing us, and maybe also yourself. It still seems to me you are re-discovering the well-known dependency problem. If you are making the point that naive "one operation at a time" computing can never overcome this problem, I think we would all agree with you. To solve it, you need to argue at a higher mathematical level before you start doing arithmetic.

Could you please give a *definition* of the terms
  restoration issue,
  self-reduction issue?
Something like "In some general situation XXX, if we want to compute YYY and we actually get ZZZ, that's the restoration issue". Trying to define them by example is not sufficient.

Also, I support what Walter Mascarenhaus said: program this approach as software -- a simple prototype will do, say in Matlab -- and let's see how useful it is.

Regards

John Pryce