Re: standardizing Taylor arithmetic, etc.
I agree with Arnold's assessment that, to obtain a clear standard
in a reasonable amount of time, we should focus on basics. I also
agree with the rationale he gives for our work.
Baker
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Arnold Neumaier wrote:
Taylor arithmetic is a model for operating with uncertain _functions_,
not one for operating with intervals, interpreted as uncertain
_numbers_. Thus the standard should have to say nothing about it.
It doesn't make sense to standardize all possible formats that people
used in the past (or might use in the future) to get interval
enclosures.
The task is only to standardize interval arithmetic, such that others
who define more complex data types like Taylor models know what they
can rely upon.
If we should start catering for Taylor models we only open a can
of worms.
Then we need to look at _all_ kinds of representing functions,
various versions of centered forms, various versions of affine arithmetic,
various versions of polynomial enclosures (Taylor models
are not the only ones), etc., and we'll never reach agreement.
Arnold Neumaier
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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
Box 4-1010, Lafayette, LA 70504-1010, USA
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