6 papers
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…
Faster modular composition using two relation matrices
Vincent Neiger, Bruno Salvy, Éric Schost +1
Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem…
Effective Asymptotics of Combinatorial Systems
Carine Pivoteau, Bruno Salvy
Analytic combinatorics studies asymptotic properties of families of combinatorial objects using complex analysis on their generating functions. In their reference book on the subje…
Effective Quadratic Error Bounds for Floating-Point Algorithms Computing the Hypotenuse Function
Jean-Michel Muller, Bruno Salvy
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds…
Optimal Experimental Design for Partially Observable Pure Birth Processes
Ali Eshragh, Matthew P. Skerritt, Bruno Salvy +1
We develop an efficient algorithm to find optimal observation times by maximizing the Fisher information for the birth rate of a partially observable pure birth process involving $…
Faster Modular Composition
Vincent Neiger, Bruno Salvy, Éric Schost +1
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by ,…