An algebraic approach to the set of intervals

Details An algebraic approach to the set of intervals An algebraic approach to the set of intervals

2008-09-30

arxiv.org/abs/0809.5150v3

Mathematics

Numerical Analysis

Scientific paper

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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