A new algebraic and arithmetic framework for interval computations

TL;DR

This paper introduces a novel algebraic framework for interval arithmetic that ensures distributivity and well-defined operations, reducing wrapping effects and enabling reliable computations in applications like matrix analysis and optimization.

Contribution

It presents a new algebraic and arithmetic framework for interval computations that guarantees distributivity and well-defined operations, improving accuracy and applicability.

Findings

Framework reduces wrapping effects in interval arithmetic

Enables reliable matrix eigenvalue and inversion computations

Demonstrates applications in optimization using Python

Abstract

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python.