Sep 18 – 29, 2023
Institut Henri Poincaré
Europe/Paris timezone

Efficient approximation of polynomials by Guillaume Moroz

Sep 25, 2023, 2:00 PM
Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Amphithéâtre Hermite / Darboux

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris


Abstract. In modern numerical computations, real numbers are approximated with floating-point numbers, of the form s2e, where s and e are integers with a fixed precision. This representation is compact and can represent numbers with small and large magnitudes. In this talk, we will generalize this idea to approximate univariate polynomial functions with piecewise polynomials of the form s(X)Xe where s is a polynomial of fixed degree and e is an integer. Using tools such as the Newton polygon, this representation can be computed efficiently both in theory and in practice. Moreover, it can be used to efficiently evaluate and find roots approximations of a high-degree polynomial.

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