RE: Motion P1788/M0037.01:MidAndRadSpecs --- voting period begins
I vote YES (of course)
-----Original Message-----
2012/10/20 Ralph Baker Kearfott <rbk@xxxxxxxxxxxx <mailto:rbk@xxxxxxxxxxxx>>
PP-1788:
The voting period herewith
begins. Voting will continue until after Saturday, November 10, 2012.
Voting on this motion will proceed according to the rules for
position papers (quorum and simple majority).
Comment can continue during voting, but the motion
cannot be changed during voting.
Juergen: Please update the web page with this action.
Acting secretary: Please record the transaction in the minutes.
The motion appears in the private area of the IEEE P-1788 site:
http://grouper.ieee.org/__groups/1788/private/Motions/__AllMotions.html <http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html>
I have also attached the motion, for your convenience.
As usual, please contact me if you need the password to the private
area.
Best regards,
Baker (acting as chair, P-1788)
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This motion about midpoint and radius is based on the
discussions during our 2012 annual meeting at SCAN'2012,
specifically on the idea proposed by Siegfried Rump:
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Definition of the _midpoint_ of an interval [a,b]:
* we compute the mathematical midpoint
(a + b) / 2 in the extended real line (whenever it is
possible), and then take a finite computer representable
floating point number which is the closest to this mathematical
midpoint; if there are two closest numbers, we use rounding to
even, i.e., select the one whose binary expansion ends in 0
* the only interval for which the mathematical midpoint is not
defined is the interval (-oo, +oo); for this interval, natural
symmetry prompts us to define the midpoint as 0;
Examples:
* for an interval [a, +oo) with finite a, the midpoint is the
number closest to +oo, i.e., MAXREAL
* for an interval (-oo, a) with finite a, the midpoint is the
number closest to -oo, i.e., -MAXREAL
* for an interval [1, 1 + u], where 1 + u is the number closest
to 1, the mathematical midpoint is 1 + (u / 2), so the closest
numbers are 1 and 1 + u; rounding to even results in 1 being
the desired midpoint
Please note that a midpoint is, in general, different from a
bisection point used to bisect an interval in different
interval algorithms
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For any interval [a, b], once its midpoint m is defined, we can
define its _radius_ r as the smallest computer representable
floating point number (finite or infinite) for which the
interval [m - r, m + r] contains the original interval [a, b].
Examples:
* for the interval [1, 1 + u], the radius is u
* for the intervals [a, + oo) and (-oo, a), the radius is oo;
this example shows the need for using an infinite number.
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx <mailto:rbk@xxxxxxxxxxxxx> (337) 482-5346 <tel:%28337%29%20482-5346> (fax)
(337) 482-5270 <tel:%28337%29%20482-5270> (work) (337) 993-1827 <tel:%28337%29%20993-1827> (home)
URL: http://interval.louisiana.edu/__kearfott.html <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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