An algebraic approach to the set of intervals

2008/09/30 by Nicolas Goze, Goze, Nicolas, Elisabeth Remm +1
Computer Science · Mathematics · #65G30 #65G40 #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematics and Applications #Numerical Analysis (math.NA) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0809.5150

openalex publication_date 2008/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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