Symbolic-Numeric Tools and Applications

by Mioara Joldes (LAAS-CNRS)

Thursday Feb 13, 2025, 4:00 PM → 6:00 PM Europe/Paris

Bat 1R2 salle 207

When computing with finite precision, one strives to achieve accurate and/or guaranteed results without compromising efficiency. For this, we combine symbolic and numerical computation, which leads to the development of specific new approximation algorithms.

This talk will survey some symbolic-numeric tools used for the reliable evaluation in fixed-precision of elementary and special functions. We make important use of computer algebra algorithms on D-finite functions --i.e., solutions of linear differential equations with polynomial coefficients-- to evaluate these functions as sums of series whose coefficients are produced by linear recurrence relations, specifically designed to avoid cancellation issues.

The particular example of the computation of the orbital collision probability between a space debris and a satellite will be presented.

Finally, these results are put in perspective: when addressing practical space security and sustainability challenges, the goal is to develop more efficient and reliable software routines for generic numerical problems arising in this domain.

This is based on joint works with D. Arzelier, F. Bréhard, J.B. Lasserre, M. Mezzarobba, B. Salvy, R. Serra.