Re: A mid-rad interchange motion...
This is somewhat reminiscent of the staggered arithmetic techniques
used, for example, to achieve rapid, "almost accurate" dot products
in software with 754 numbers. Is that the underlying sense (that is, roughly, to use
two floating point datums, or possibly two datums with
different precisions) to represent the radius?
Baker
On 5/16/2010 05:08, Arnold Neumaier wrote:
Dan Zuras Intervals wrote:
From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
- Define an interval type to be an inf-sup or mid-rad type depending
on its level 3 representation:
An inf-sup interval type is one whose level 3 representation by
floating-point numbers lets the lower and upper bound of each
nonempty interval of that type be retrieved exactly.
and
A mid-rad interval type is one whose level 3 representation by
floating-point numbers lets the midpoint and radius of each
nonempty [add "bounded" here?] interval of that type be retrieved
exactly.
Letting level 3 drive the definition looks perverse, but it seems
to me that's where the essence of the two kinds of type lies.
It looks perverse to me as well. I think of the
distinction as living at the set of values each
form represents. Therefore, level 1.
However, I'm not sure whether a "mid-rad1-rad2" type admits a
definition on these lines, because of the extra degree of freedom
in describing it by 3 numbers instead of 2.
Actually, one should think of "mid-rad1-rad2" as center+error-interval,
thus it is composed of two objects, a center and an error interval,
possibly of different precisions.
--
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R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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