Publicaties

A new measure called min-max elementwise backward error is introducedfor approximate roots of scalar polynomials $p(z)$.Compared with the elementwise relative backward error, this new measure allows forlarger relative perturbations on the coefficients of $p(z)$ that do not participate muchin the overall backward error.By how much these coefficients can be perturbed is determinedvia an associated max-times polynomial and its tropical roots.An ...

The problem of computing recurrence coefficients of sequences of rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue problem for a pencil of Hessenberg matrices. Two procedures are proposed to solve this inverse eigenvalue problem, via the rational Arnoldi iteration and via an updating procedure using unitary similarity transformations. The latter is shown to be numerically stable. This ...

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 ...

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 ...

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 ...