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Re: Motion 31 - incorporating Complete Formats into the standard

Am 13.02.2012 01:02, schrieb Dan Zuras Intervals:

Subject: Re: Motion 31 - incorporating Complete Formats into the standard
From: John Pryce<j.d.pryce@xxxxxxxxxxxx>
Date: Sun, 12 Feb 2012 22:13:33 +0000
To: stds-1788<stds-1788@xxxxxxxxxxxxxxxxx>

P1788

Before re-submitting the Level 1 text I need some answers relating to motion 9...

. . .

Regarding "exact" vs "accurate" or "faithful" dot product,

The position paper I have is "The Exact Dot Product as Basic Tool for Long
Interval Arithmetic" by Ulrich Kulisch and Van Snyder (UKVS for short),
which seems to be written very much as a spec, since it contains "An
implementation shall ..." sentences.


I think that P1788 should not do the job of 754...

. . .


	Let me comment on just these two issues before you.

	In principle, I agree with whoever said 1788 should
	not do 754 things again.  And, indeed, you will find
	the dot products&  related reductions as optional in
	clause 9.4 of 754-2008.

	Alas, we could not agree on making them mandatory&
	we could not agree on an accuracy policy.

	So if 1788 made them both mandatory&  exact (as Ulrich
	wishes) it would not be repeating anything from 754.

	My second comment is really a question.  I am familiar
	with the uses of Ulrich's dot product in the context
	of linear floating-point problems.  But I am not
	familiar with how they are used in the interval world.
Dan: In a hurry I copied a section of my book (Computer Arithmetic and Validity, de Gruyter 2008). The section is entitled: Multiple Precision Interval Arithmetic. See the attachment. A look at the formulas shows that the exact dot product is used again and again. 
Best regards, Ulrich

	Are they used in the same way as in floating-point by
	using a mid-rad form to compute interval results by
	means of an accurate vector or matrix midpoint together
	with a Jacobian for the radii?

	Or does one just do a dot product in the inf elements
	&  another on the sup elements to get a narrower dot
	product on a vector of intervals in some context that
	may be entirely unrelated to linear problems?

	I ask partly for my own sake&  partly because the
	answer might drive your own efforts.


				Dan




--
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik (IANM2)
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch

Telefon: +49 721 608-42680
Fax: +49 721 608-46679
E-Mail: ulrich.kulisch@xxxxxxx
www.kit.edu
www.math.kit.edu/ianm2/~kulisch/

KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gemeinschaft

Attachment: LongInterval.pdf
Description: Adobe PDF document