An algebraic approach to the set of intervals (a new approach of arithmetic of intervals)
arXiv:0809.51736 citationsh-index: 15
Originality Incremental advance
AI Analysis
This work provides a new theoretical framework for interval arithmetic, but its practical impact is unclear due to lack of empirical validation.
The paper presents intervals as a normed vector space and defines a four-dimensional associative algebra for interval multiplication, enabling divisibility and differential calculus. No concrete numerical results are reported.
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.