An algebraic approach to the set of intervals (a new approach of arithmetic of intervals)

2008/09/30 by Nicolas Goze, Goze, Nicolas, Elisabeth Remm +1
Computer Science · #FOS: Mathematics #G.1.0 #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.0809.5173

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

Abstract

In this paper 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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