Description
Date depot: 30 mars 2025
Titre: Optimization of the representation of results in interval arithmetic and applications
Directeur de thèse:
Stef GRAILLAT (LIP6)
Domaine scientifique: Sciences et technologies de l'information et de la communication
Thématique CNRS : Calcul arithmétique et formel, codage et cryptologie
Resumé: This thesis focuses on improving the efficiency and reliability of numerical computations using interval arithmetic, a method that represents real numbers as intervals to rigorously account for rounding errors. The main contribution is the development of a "compressed" format enabling the representation of intervals with reduced memory usage. The work includes creating a new interval arithmetic library for single, double, and multiple precision arithmetic, comparing it with existing libraries like MPFI and INTLAB. The study also explores applications in self-validating methods and examines parallels with Posit arithmetic to enhance numerical reliability in large-scale simulations.