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Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]

Dan Zuras Intervals wrote:


	If we are to pursue this at this time, please include accurate
	versions of all of sum, dot product, sum of squares, & sum of
	absolute values for all supported precisions.

	That the sum is needed is obvious.

	The sum of squares is needed for an accurate 2-norm & is
	different than calling dot product with the same argument
	twice in ways that are important in our context.

	The sum of absolute values is needed for a 1-norm & is pretty
	cheap once you have an accurate sum.


Yes, these are useful. Perhaps also the 2-norm itself!



	Finally, let me caution you that how these things behave on
	empty & NaI elements may turn out to be important to this
	group.
I think only interval-valued results for noninterval inputs should be provided by the standard. Then there are no problems. 

If some element is NaN or two terms in the sum are +inf and -inf,
the result should be the empty set; otherwise the tightest enclosing
interval of the exact result should be returned.


Arnold Neumaier