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

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Goze, Nicolas
Remm, Elisabeth
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Abstract
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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.
Keywords
Mathematics - Numerical Analysis, G.1.0
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