Paper on interval arithmetic

["Siegfried M. Rump" <rump@xxxxxxxxxxxxx>]

Dear P1788 members,

To my knowledge all definitions of interval arithmetic start with real endpoints
and prove properties. For a practical use the definition is then specialized to
finitely many endpoints, where many of the mathematical properties are no
longer valid. There seems no treatment how to choose this finite set of endpoints
to preserve as many mathematical properties as possible.

In the enclosed paper necessary and sufficient conditions on the set of endpoints
are developed to ensure desirable mathematical properties. Among others, problems
with infinite endpoints are addressed. I think it is hazardous to allow endpoints
which are not member of any interval.

The new scheme can be implemented using the IEEE~754 floating-point format.
Mathematical properties hold true which are not valid for other definitions of
interval arithmetic, even not with infinitely many endpoints.

Best wishes,

Siegfried M. Rump

--
=====================================================
Prof. Dr. Siegfried M. Rump
Institute for Reliable Computing
Hamburg University of Technology
Schwarzenbergstr. 95
21071 Hamburg
Germany
phone +49 40 42878 3027
fax +49 40 42878 2489
http://www.ti3.tu-harburg.de

and

Visiting Professor at Waseda University
Faculty of Science and Engineering
3-4-1 Okubo, Shinjuku-ku
Tokyo 169-8555
Japan
phone/fax in Japan +81 3 5286 3330

Attachment: IVarithmeticSubmitted.pdf
Description: Adobe PDF document