1 citations · 1 across the 5 of their papers we have counts for
6 papers
Mixed precision Newton's method for optimization
Nicolas Brisebarre, Giuseppe Carrino, Theo Mary +1
Second-order optimization methods, such as Newton's algorithm, achieve fast local convergence and high accuracy, but their practical use is often limited by high computational cost…
Integer points close to a transcendental curve: an algorithmic approach
Nicolas Brisebarre, Guillaume Hanrot
In this article, we propose an algorithmic approach to determine the integer points located near a transcendental curve. This approach is closely related to a celebrated work by Bo…
Fractions of Recurrence Operators for Generalized Fourier Series in Classical Orthogonal Polynomials
Alexandre Benoit, Nicolas Brisebarre, Bruno Salvy
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients…
Differential-Difference Properties of Hypergeometric Series
Nicolas Brisebarre, Bruno Salvy
Six families of generalized hypergeometric series in a variable and an arbitrary number of parameters are considered. Each of them is indexed by an integer . Linear recurren…
On a two-valued sequence and related continued fractions in power series fields
Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias
We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a gen…
Finding the "truncated" polynomial that is closest to a function
Nicolas Brisebarre, Jean-Michel Muller
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial…