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

Ralph Baker Kearfott wrote:

Arnold,

Thank you for your input and clarification.  Are there
additional comments concerning this?  Should mid-rad be
standardized as an optional type?

Baker

On 5/10/2010 08:26, Arnold Neumaier wrote:

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.
I don't know what definitions Intlab uses, but by (39) in http://grouper.ieee.org/groups/1788/Material/Markov_scan06.pdf, multiplication of mid-rad intervals gives the same bounds and/or range enclosure as inf-sup, e.g., mid-rad gives (1,1)*(1,1)=(2,2) which is [0,2]*[0,2]=[0,4] in inf-sup. 





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.


I don't understand... why would it not conform?

Nate