Re: A late question Re: P1788.1/M001.01: voting period begins
All,
After pondering over the use of “natural interval extension” in the standard, I do not see
problems with this term and inconsistencies in the standard. True, this term has been
used to mean “replace reals by intervals and do interval operations”, but this is more about
interval evaluation rather than a mathematical definition.
If we simply use “range”, we miss the case when the function is discontinuous.
Regards,
Ned
> On Dec 2, 2015, at 8:14 AM, Ralph Baker Kearfott <rbk5287@xxxxxxxxxxxxx> wrote:
>
> All,
>
> I know there is a process for submitting errata to standards. This
> may be easy, since we would only be changing terminology, not normative
> substance. I'll investigate this with regard to 1788.
>
> Regarding 1788.1, I like Vladik's suggestion to simply use "range" for
> this concept.
>
> Best regards,
>
> Baker
>
> On 12/01/2015 09:46 PM, Kreinovich, Vladik wrote:
>> I googled for "natural interval extension", the first link is to Wikipedia page on interval computation, which gives exactly the same definition as Baker mentioned -- the result of applying naïve interval arithmetic to the original expression
>>
>> If I understand Ned correctly, while this problem surfaced only now, the same somewhat confusing terminology is used in the already approved 1988 standard, so if we change the definition of natural extension in the new simplified standard, we will get a contradiction with the original 1788 text.
>>
>> So why don't we just call it the range, and avoid using the potentially confusing term "natural interval extension"?
>>
>> P.S. Now I understand why one of the students in my recent graduate interval computations class, in one of his assignments, used the term "natural interval extension" not in the sense that I taught (via straightforward application of interval arithmetic), but as a synonym for range. I was not happy with this, and got confused, but looks like he was more attentive than I was in reading some of my handouts :-(
>>
>> -----Original Message-----
>> From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Nedialkov, Ned
>> Sent: Tuesday, December 01, 2015 11:30 AM
>> To: Ralph Baker Kearfott <rbk5287@xxxxxxxxxxxxx>
>> Cc: Stds-1788 <stds-1788@xxxxxxxx>
>> Subject: Re: A late question Re: P1788.1/M001.01: voting period begins
>>
>> Baker et al,
>>
>>> On Dec 1, 2015, at 7:38 AM, Ralph Baker Kearfott <rbk5287@xxxxxxxxxxxxx> wrote:
>>>
>>> Ned et al,
>>>
>>> Ouch! I fear I have been truant in reading this.
>>> At the beginning of 4.4.4, Rge(f | \x) is used in defining the natural
>>> interval extension. Is this notation defined elsewhere in the
>>> document,
>>
>>
>> on the previous page
>>
>>> and does this mean the range of f
>>> over \x?
>>
>> Yes.
>>
>>> If so, the term natural interval extension is used differently from
>>> the way I have seen it used most often.
>>> (My idea of "natural interval extension" is to simply plug in the
>>> interval and do the interval arithmetic, thus resulting in an
>>> overestimation, due to interval dependency, of the range.
>>> The term I have seen used most often for the range of f is the "united
>>> extension," as in e.g. Ratschek and Rokne's book.
>>>
>>
>> I am afraid you are right. I tried to be consistent with the full standard, but I also had the same question. Any thoughts by others?
>>
>> Regards,
>> Ned
>>
>
>
> --
>
> ---------------------------------------------------------------
> Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
> (337) 482-5270 (work) (337) 993-1827 (home)
> URL: http://interval.louisiana.edu/kearfott.html
> Department of Mathematics, University of Louisiana at Lafayette
> (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
> Box 4-1010, Lafayette, LA 70504-1010, USA
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>