Vitae for Nathalie Revol

Floating-Point Arithmetic

A Taylor Function Calculus for Hybrid System Analysis: Validation in Coq

We present a framework for the verification of the numerical algorithms used in Ariadne, a tool for analysis of nonlinear hybrid system. In particular, in Ariadne, smooth functions are approximated by Taylor models based on sparse polynomials. We use the Coq theorem prover for developing Taylor models as sparse polynomials with floatingpoint coefficients. This development is based on the formal...

Reliable Implementation of Real Number Algorithms: Theory and Practice Dagstuhl Seminar

From 08.01.06 to 13.01.06, the Dagstuhl Seminar 06021 Reliable Implementation of Real Number Algorithms: Theory and Practice was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as ...

Implementing Taylor models arithmetic with floating-point arithmetic

The implementation of Taylor models arithmetic may use floating-point arithmetic to benefit from the speed of the floatingpoint implementation. The issue is then to take into account the roundoff errors. Here, we assume that the floating-point arithmetic is compliant with the IEEE-754 standard. We show how to get tight bounds of the roundoff errors, and more generally how to get high accuracy f...

Multiple Precision Interval Packages: Comparing Different Approaches

We give a survey on packages for multiple precision interval arithmetic, with the main focus on three specific packages. One is within a Maple environment, intpakX, and two are C/C++ libraries, GMP-XSC and MPFI. We discuss their different features, present timing results and show several applications from various fields, where high precision intervals are fundamental.