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Re: mid-rad, inf-sup, a caution...

Ralph Baker Kearfott wrote:

I point out again that mid-rad is an important component
"under the hood" of INTLAB, which I perceive to be the
most widely-used interval package.  (Again, correct me
if this statement is inaccurate.)



Only in two cases:

- for large and matrices with narrow entries, and even then
  the representation is created on the fly and not used for storing
  intervals.
  For wide intervals, there is significant overestimation, and not
  even the sign of a product is preserved: [0,2]*[0,2]=[-2,4]
  in the centered midrad arithmetic used in Intlab (though not for
  1x1 matrices.
- for complex intervals (which was already agreed to be outside the
  scope of 1788.)

In particular, even if 1788 would forbid midrad data types,
Intlab would still be conforming, while if midrad operations
were required, Intlab would no longer conform.


Arnold Neumaier