More Re: overflow question
Along these lines, a logical thing that comes to mind
is to choose as midpoint of a positive semi-infinite interval
the geometric mean of the lower bound and MAXREAL,
to try to get the same number of floating point numbers
in each half. However, I'm not saying we standardize
this; this seems to be a research topic (minor or not).
It is my personal opinion that we should standardize things
that are already well-understood and for which there will
be a universal benefit for everyone to be doing it the
same way.
Baker
Arnold et al,
On 05/10/2012 05:17 AM, Arnold Neumaier wrote:
.
.
.
But this midpoint is useless. Your bisection algorithm will
spend most time exploring a tiny neighborhood of infinity.
Ah, yes. That is certainly a valid point of view if the
function, say, has a limit or a solution at infinity; in
such cases, the best solution to the user's problem
might be for the person posing
the problem to map the domain into a finite, closed
interval, with one end point corresponding to infinity.
In that context, bisecting a semi-infinite interval at
MAXREAL is like producing an interval whose end points
are consecutive floating point numbers.
Baker
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