Re: Kaucher intervals
Michel Hack schrieb:
It would have helped if early on we had seen a concise, though perhaps
incomplete, description of Kaucher intervals
I want to call attention to my manuscript
A. Neumaier,
Computer graphics, linear interpolation, and nonstandard
intervals
http://www.mat.univie.ac.at/~neum/ms/nonstandard.pdf
which accompanies the Vienna Proposal.
There a concise definition and discussion of Kaucher arithmetic,
modal arithmetic, and their uses is given. (Also, it is pointed out
that there is a slight difference between Kaucher arithmetic and
modal arithmetic for binary operations that are not commutable.
This might affect atan2 - I didn't check.)
One also needs a clear definition of the behavior for Kaucher intervals
of partially defined functions such as the square root.
To my knowledge, no such definition is avaliable in the literature.
Arniold Neumaier