# Publications

## Solving Systems of Polynomial Equations KU Leuven

Systems of polynomial equations arise naturally from many problems in applied mathematics and engineering. Examples of such problems come from robotics, chemical engineering, computer vision, dynamical systems theory, signal processing and geometric modeling, among others. The numerical solution of systems of polynomial equations is considered a challenging problem in computational mathematics. Important classes of existing methods are algebraic ...

## Numerical root finding via Cox rings KU Leuven

## Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers KU Leuven

## Non-unitary CMV-decomposition KU Leuven

## Uniform approximation on the sphere by least squares polynomials KU Leuven

The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of $\RR^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere.
First we focus on least squares polynomial approximation and prove that the related Lebesgue constants w.r.t.\ the uniform norm grow at the optimal rate. Then, we consider delayed arithmetic means of least squares polynomials ...

## Preface KU Leuven

## Biorthogonal rational Krylov subspace methods KU Leuven

A general framework for oblique projections of non-Hermitian matrices onto rational Krylov subspacesis developed. To obtain this framework we revisit the classical rational Krylov subspace algorithm and prove that theprojected matrix can be written efficiently as a structured pencil, where the structure can take several forms such asHessenberg or inverse Hessenberg. One specific instance of the structures appearing in this framework for ...

## Truncated Normal Forms for Solving Polynomial Systems KU Leuven

© 2018 Association for Computing Machinery.All Rights Reserved. In this poster we present the results of [10]. We consider the problem of finding the common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to find the solutions and to compute the structure of the quotient ring R/I from the cokernel of a resultant map. This leads to what we call ...