Publications
Chosen filters:
Chosen filters:
Generation of orthogonal rational functions by procedures for structured matrices KU Leuven
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 ...
Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder KU Leuven
A new measure called min-max elementwise backward error is introduced for approximate roots of scalar polynomials $p(z)$. Compared with the elementwise relative backward error, this new measure allows for larger relative perturbations on the coefficients of $p(z)$ that do not participate much in the overall backward error. By how much these coefficients can be perturbed is determined via an associated max-times polynomial and its tropical roots. ...
Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms KU Leuven
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 ...