Re: MidRad to/from InfSup (was: the "set paradigm" is harmful)
Kearfott Ralph B schrieb:
Svetoslav and P1788:
Yes, IF we decide to include midpoint-radius (something that
should be formally decided before we formally decide on HOW
to include them), we may want to avoid specifications of
edge cases. (I haven't seen a formal second to the motion
to include midpoint /radius, unless I have missed something.)
If we avoid "edge cases," specifying what is a "narrow" interval
might be as messy as including edge cases.
With whatever definition of narrow, there will be narrow intervals
a,b such that a+b is not narrow, so the resulting arithmetic will
result in lots of exceptions.
This was just one of the things we want to avoid by having a good standard.
I recommend strongly against including arithmetic on midrad intervals
into the standard.
For operations with single intervals, operations with the midrad
representation have nothing to recommend.
Note that the use of midrad as _intermediates_ in an interval
_matrix_ package (as provided by Intlab) will not be affected by
the standard, since the standard will most likely not specify
how matrix operations are to be carried out.
Arnold Neumaier