Publicaties
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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
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers KU Leuven
Backward Error Measures for Roots of Polynomials KU Leuven
We analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error introduced by Mastronardi and Van Dooren, and the tropical backward error introduced by Tisseur and Van Barel. We show that these measures are equivalent under suitable assumptions. We also show relations between these measures and the classical element-wise and ...