This paper is concerned with approximations of the Boltzmann equation based on the
method of moments. We propose a generalization of the setting of the moment-closure …

Abstract Systems of polynomial equations arise frequently in computer vision, especially in
multiview geometry problems. Traditional methods for solving these systems typically aim to …

This is the first book that focuses on practical algorithms for polynomial inequality proving
and discovering. It is a summary of the work by the authors and their collaborators on …

We give an explicit upper bound for the algebraic degree and an explicit lower bound for the
absolute value of the minimum of a polynomial function on a compact connected component …

We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …

We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …

Subdivision-based algorithms recursively subdivide an input region until the smaller
subregions can be processed. It is a challenge to analyze the complexity of such algorithms …

Consider a polynomial optimization problem. Adding polynomial equations generated by the
Fritz John conditions to the constraint set does not change the optimal value. As proved in …

We present a purely numerical (ie, non-algebraic) subdivision algorithm for computing an
isotopic approximation of a simple arrangement of curves. The arrangement is “simple” in …

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 …