An algebraic approach to the set of intervals
This work provides a foundational mathematical reformulation of interval arithmetic, potentially benefiting fields relying on interval computations, but the abstract lacks concrete performance numbers or comparisons.
The paper introduces a new algebraic framework for interval arithmetic, representing intervals as a normed vector space and defining a four-dimensional associative algebra for interval multiplication, enabling divisibility and differential calculus.
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.