Wolff von Gudenberg, Jürgen
Interval Arithmetic and Standardization
Abstract
Interval arithmetic is arithmetic for continuous sets. Floatingpoint intervals are intervals of real numbers with floatingpoint bounds.
Operations for intervals can be efficiently implemented. There is an unanimous agreement, how to define the basic operations,
if we exclude division by an interval containing zero. Hence, it should be standardized.
For division by zero, two options are possible, the clean exception free interval arithmetic or the containment arithmetic.
They can be standardized as options.
Elementary functions for intervals can be defined. In some application areas loose evaluation of functions,
i.e. evaluation over an interval which is not completely contained in the function domain, is recommended,
In this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable in that case.
BibTeX  Entry
@InProceedings{wolffvongudenberg:DSP:2008:1434,
author = {J{\"u}rgen Wolff von Gudenberg},
title = {Interval Arithmetic and Standardization},
booktitle = {Numerical Validation in Current Hardware Architectures},
year = {2008},
editor = {Annie Cuyt and Walter Kr{\"a}mer and Wolfram Luther and Peter Markstein},
number = {08021},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1434},
annote = {Keywords: Intervals, containment sets, IEEE754r}
}
Keywords: 

Intervals, containment sets, IEEE754r 
Seminar: 

08021  Numerical Validation in Current Hardware Architectures

Issue date: 

2008 
Date of publication: 

22.04.2008 