| keyword(s) : Corps finis – Racines primitives – Attaques par perturbation – Espaces de matrices pour les codes correcteurs – Algèbre linéaire exacte intensive – Systèmes dynamiques hybrides – Algorithmes symboliques-numériques – Parallélisme multi-coeurs – Conception et modélisation logicielle – Computer Algebra patterns. |
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| Contributions to high-performance computer algebra |
| Scientific computing is often associated with numerical computation. Yet in many scientific disciplines it is necessary to go beyond the approximations: need for certification of results, computation over discrete mathematical structures, numerical algorithm instability. Computer algebra therefore strive to give accurate or certified results. Now, the main obstruction to the use of symbolic computation is often the poor performance of commercial systems even on fundamental operations such as linear algebra. The goal of this work is to reduce the gap between exact and numerical computations, both in the algorithm and the software sides. The challenges are numerous: developing an effective arithmetic for discrete structures; designing algorithms with optimal leading terms of complexity, taking into account the growth of intermediate data; transcribing these algorithms in software that combines perennial efficiency, interfacing and genericity. |
| english keyword(s) : Finite fields – Primitive roots – Perturbation attacks – Subspaces of matrices for error-correcting codes – High-performance exact linear algebra – Hybrid dynamical systems – Symbolic-numeric algorithms – Multi-core parallelism – Software design and modelization – Computer Algebra patterns. |
