In modern numerical computations, real numbers are approximated with floating-point numbers, of the form $s2^e$, 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 $s(X)X^e$ 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.
De Joachim von zur Gathen
De Sébastien Tavenas
De Pranjal Dutta
De Nitin Saxena
De Clément Pernet
De Fredrik Johansson
De Lihong Zhi
De Annie Cuyt
De Juan Camilo Arosemena Serrato
De Giuseppe Savaré
De Juan Camilo Arosemena Serrato
De Amine Marrakchi
De Shirly Geffen
De Francesca Arici
