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

Dan (and Chenyi, if I may step in),
Cancellation is when you create a sum \sum x_i and need \sum_{i\ne j} x_i. You then subtract x_i from the sum, but you do it in such a way that there isn't overestimation, that is, we get, to within roundout error, the same interval as we would have if we had omitted x_j from the original sum. This is useful, e.g. in Gauss--Seidel iteration. 

For example, cancellation produces x \cancelminus x = [0,0]
The operation is subtraction, where it is assumed that, in the resulting interval, every point value in the first operand must be equal to every point value in the second operand in forming the set of all possible results. (That is, we assume dependency.)
Of course, there's a very simple operational definition in terms of the end points :-) 

How did I do with the explanation, Chenyi?

Baker

Dan Zuras Intervals wrote:

Date: Thu, 10 Sep 2009 10:47:43 -0500
From: "Chenyi Hu" <chu@xxxxxxx>
To: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>,
	"Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
Cc: "James Demmel" <demmel@xxxxxxxxxxxxxxx>,
	"Nathalie Revol" <Nathalie.Revol@xxxxxxxxxxx>,
	<stds-1788@xxxxxxxxxxxxxxxxx>,
	"Ronald Boisvert" <boisvert@xxxxxxxx>,
	"Arnold Neumaier" <Arnold.Neumaier@xxxxxxxxxxxx>
Subject: Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE
	Interval Standards Working Group]

Dan, et al,

Just for your information, about a decade ago, Jim and I were on the
BLAST working group led by Jack. That group tried to establish an Interval
BLAS standard including BLAS-1, -2, and -3. The final document is available
at http://www.netlib.org/blas/blast-forum/chapter5.pdf. Also, my former
graduate student Michael Nooner made a reference implementation which is
available at http://www.cs.uca.edu/interval/intbox/ with documentation. We
further described the design and implementation as chapter 10 in the book
"Knowledge Processing with Interval and Soft Computing" published by
Springer last year. Since we did not have a standard on interval computing,
 the  Interval BLAS was listed under Journal of Development in the final
document of BLAST.

Regards,

Chenyi



	Cool.

	I notice a basic interval operation called 'cancellation'
	that I haven't heard others speak of.  At least not by
	that name.  Can you give me a brief explanation of what
	its used for?

	Other than issues involving the increment & length integers
	having values <=0 & the occasional mention of empty on
	intersection, I see no mention of exceptional behavior.
	That is, the behavior of these routines when presented
	with exceptional interval elements.

	Is this because exceptional interval behavior is not
	considered or that such behavior is described elsewhere?

	I ask because, as a standards body, we spend an inordinate
	amount of time concerning ourselves with such things.  Far
	more than our users need to.  And I am curious if this work
	has given you any insights into exceptional behavior that
	would help us in designing the standard.

	Operations on vectors & matrices with elements such as NaI,
	empty, or even an interval element of infinite width could
	affect the whole result, just a column or row, or perhaps
	only an element or two.

	Are such things handled gracefully or just punted?

	What would you advise US to do?

	Could your work form the basis for an interval BLAS in 1788
	or should we use it as a starting point for something else?

	Thanks,

				Dan