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Re: this is how I understand John Pryce's result re decorations



Hi Vladik,

IMHO, it seems you understand the most important aspects, particularly when you say about straightforward interval computation:

"The resulting enclosure is often too wide. There exist much more efficient
techniques (such as the mean value form); see, e.g., [1]. However, straightforward interval computation is important, since most efficient techniques for computing the desired range y use straightforward interval computations on intermediate steps."

In my perspective, it is straightforward computation that is within the scope of IEEE 1788 to standardize. Other techniques that can often give better enclosures, such as mean value form, expression rearrangement, monotonicity and/or endpoint analysis, etc. still remain very valuable aspects of interval computations. But as those who have experience implementing interval computations can attest to, there is no such technique that works all the time, and often these techniques require the assistance of Computer Algebra Systems. I think it is too big a problem for P1788 to try and standardize those various methods.

On the other hand, it is the straightforwad computations on intermediate steps that can be implemented efficiently at the hardware level in an interval processor, as well as the neccesary property tracking with decorations. So I believe IEEE 1788 has a potential to be a very successful standard if it concentrates on this aspect.

Sincerely,

Nate



----- Original Message ----- From: "Kreinovich, Vladik" <vladik@xxxxxxxx>
To: <stds-1788@xxxxxxxx>
Sent: Saturday, May 21, 2011 4:29 PM
Subject: this is how I understand John Pryce's result re decorations


I think I understand, I may be wrong, but at least I seem to understand now what was not clear to me from the very beginning: how the decorations that are defined for _functions_ are somehow attached to _intervals_; see attached.