An algebraic approach to the set of intervals
Numerical Analysis
2009-10-22 v3
Abstract
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility and in some cases an euclidian division. We introduce differential calculus and give some applications.
Cite
@article{arxiv.0809.5150,
title = {An algebraic approach to the set of intervals},
author = {Nicolas Goze and Elisabeth Remm},
journal= {arXiv preprint arXiv:0809.5150},
year = {2009}
}