39 citations · 92 across the 20 of their papers we have counts for
7 papers · 1 filter
Fast evaluation and root finding for polynomials with floating-point coefficients
Rémi Imbach, Guillaume Moroz
Evaluating or finding the roots of a polynomial with floating-point number coefficients is a ubiquitous problem. By using a piecewise approximation…
New data structure for univariate polynomial approximation and applications to root isolation, numerical multipoint evaluation, and other problems
Guillaume Moroz
We present a new data structure to approximate accurately and efficiently a polynomial of degree given as a list of coefficients. Its properties allow us to improve the sta…
Fast real and complex root-finding methods for well-conditioned polynomials
Guillaume Moroz
Given a polynomial of degree and a bound on a condition number of , we present the first root-finding algorithms that return all its real and complex roots with a nu…
Evaluation of Chebyshev polynomials on intervals and application to root finding
Viviane Ledoux, Guillaume Moroz
In approximation theory, it is standard to approximate functions by polynomials expressed in the Chebyshev basis. Evaluating a polynomial of degree n given in the Chebyshev bas…
A Fast Algorithm for Computing the Truncated Resultant
Guillaume Moroz, Éric Schost
Let P and Q be two polynomials in K[x, y] with degree at most d, where K is a field. Denoting by R K[x] the resultant of P and Q with respect to y, we present an algorithm to…
Fast polynomial evaluation and composition
Guillaume Moroz
The library \emph{fast\_polynomial} for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as Hörner, divide and co…