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Re: Up-to date Interval Arithmetic



Ulrich,

I think Walter is correct.

I would interpret “rigor” in this context as, “Thou shalt not lie.”  Containment is a requirement to be considered “interval”.  Any violation of containment is an implementation error.  I observe that much of the discussion in this P1788 group has been about defining exactly what we mean by “containment” in extreme cases.

Of course, we prefer tight bounds to loose ones, but often, there is a trade-off of tightness with “cost”, in some sense, on someone’s part.  Other threads of the discussion in this P1788 group have been about the extent to which the standard should prescribe preferences on the tightness/cost (in some sense to someone) spectrum.

George Corliss



On Mar 27, 2015, at 7:09 AM, Walter Mascarenhas <walter.mascarenhas@xxxxxxxxx> wrote:

Dear Ulrich,

   I have the impression that your answer confuses "rigor" with
"tightness", but English is not my mother tong and I may be the
confused one.

   According to my understanding of the English words, traditional
interval arithmetic is perfectly "rigorous", in the sense that it will
not lead you to wrong conclusions.

  It may not be "tight", in the sense that it may
lead you to no conclusions in situations in which you
could get answers by other methods.

  Which words would a native speaker use to express these
two, distinct, concepts?

             regards,

                      walter.



On Fri, Mar 27, 2015 at 8:16 AM, Ulrich Kulisch <ulrich.kulisch@xxxxxxx> wrote:
Am 26.03.2015 um 10:10 schrieb Vincent Lefevre:
On 2015-03-24 21:19:16 +0100, Ulrich Kulisch wrote:
Dear colleagues:

I attach an unpublished paper entitled:

/Up-to-date Interval Arithmetic - From closed intervals to connected sets of
real numbers//
/
which on request recently was sent to the Reliable Computing Group. You may
find it interesting.
About Unum: "It gets mathematical rigor that even conventional
interval arithmetic is not able to attain."

In what sense conventional interval arithmetic is not rigorous???

An answer to the three question marks is attached.

Best wishes
Ulrich





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