English

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.

Keywords

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}
}
R2 v1 2026-06-21T11:25:34.661Z