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Re: Bisection methods (was Re: Structured support...)

Baker Keafott wrote:

On 05/25/2012 08:33 AM, Nate Hayes wrote:

John,


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.
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As I explain in section 3.2.2, 3.2.3 and 3.2.4 the mathematical

>definition of Interval Newton, for example, is (13), but (13) is
>not an algorithm until some exact method of choosing x \in X is
>specified, e. g., (14). Same for centered forms, B&B, etc.


In the model you are proposing, only the mathematical definitions are
defined at Level 1 and Level 2, but the corresponding algorithms are not;
according to the standard, such algorithms must return NaNs.


I don't understand this.  Where in the standard (and do you mean
the current P-1788 draft?) does it say that a particular algorithm
must return a "NaN"?


Please see my May 23 e-mail and John's subsequent response. Here is the
relevant summary:

   -- The current P-1788 draft says the midpoint of an unbounded interval
is undefined at Level 1.

   -- When I asked "does this mean other interval bisection methods such as
geometric mean, smedian2, etc. are also undefined at Level 1 for unbounded
intervals?" John's answer was "yes".

   -- When I asked "does this mean all of these interval bisection methods
are undefined for unbounded intervals at Level 2, as well?" John's answer
was "yes, and let it return NaN at Level 2..."

We happen to agree with John on these points. However, this leaves many
interval algorithms undefined at Level 1 and Level 2, returning NaNs.

Nate