Re: Do I have a second? Re: a draft motion on midpoint and radius
On 2012-09-28 08:35:43 -0500, Ralph Baker Kearfott wrote:
> P-1788:
>
> Do I have a second to this motion?
I second, but I have two editorial suggestions...
> Baker
>
> On 09/28/2012 08:17 AM, Kreinovich, Vladik wrote:
> >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:
> >*******************************************************
> >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
Avoid the term "floating point". Say something like "in format F".
Ditto below, for the radius. The examples should say: inf-sup,
based on a floating-point format F.
> >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
It should be said that u > 0.
> >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
> >************************************************************
> >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.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)