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 exhibit a condition-based analysis of the adaptive subdivision algorithm due to Plantinga
and Vegter. The first complexity analysis of the\pv~ Algorithm is due to Burr, Gao and …

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used
primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this …

The condition-based complexity analysis framework is one of the gems of modern numerical
algebraic geometry and theoretical computer science. One of the challenges that it poses is …

We present the first complexity analysis of the algorithm by Plantinga and Vegter for
approximating real implicit curves and surfaces. This approximation algorithm certifies the …

Range functions are an important tool for interval computations, and they can be employed
for the problem of root isolation. In this paper, we first introduce two new classes of range …

In numerical linear algebra, a well-established practice is to choose a norm that exploits the
structure of the problem at hand to optimise accuracy or computational complexity. In …

Approximating the roots of a holomorphic function in an input box is a fundamental problem
in many domains. Most algorithms in the literature for solving this problem are conditional …

We address the problem of computing a drawing of high resolution of a plane curve defined
by a bivariate polynomial equation P (x, y)= 0. Given a grid of fixed resolution, a drawing is a …

We present a certified algorithm based on subdivision for computing an isotopic
approximation to a pair of curves in the plane. Our algorithm is based on the certified curve …