Let F (z) be an arbitrary complex polynomial. We introduce the {local root clustering
problem}, to compute a set of natural epsilon-clusters of roots of F (z) in some box region B0 …

We describe Ccluster, a software for computing natural ε ε-clusters of complex roots in a
given box of the complex plane. This algorithm from Becker et al.(2016) is near-optimal …

We present a new data structure to approximate accurately and efficiently a polynomial f of
degree d given as a list of coefficients f i. Its properties allow us to improve the state-of-the …

We describe a new algorithm Miranda for isolating the simple zeros of a
function\boldsymbolf:\mathbbR^ n →\mathbbR^ n within a box B_0 ⊆\mathbbR^ n. The …

We provide an efficient algorithm to detect whether two given trigonometric curves, ie two
parametrized curves whose components are truncated Fourier series, in any dimension, are …

In our quest for the design, the analysis and the implementation of a subdivision algorithm
for finding the complex roots of univariate polynomials given by oracles for their evaluation …

The recent advanced sub-division algorithm is nearly optimal for the approximation of the
roots of a dense polynomial given in monomial basis; moreover, it works locally and slightly …

Given a zero-dimensional polynomial system consisting of n integer polynomials in n
variables, we propose a certified and complete method to compute all complex solutions of …

Univariate polynomial root-finding has been studied for four millennia and very intensively in
the last decades. Our novel nearly optimal Las Vegas randomized root-finders approximate …

Nonrobustness refers to qualitative or catastrophic failures in geometric algorithms arising
from numerical errors. Section 45.1 provides background on these problems. Although …