3 citations · 6 across the 9 of their papers we have counts for
10 papers
Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials
Amin Faghih, Michele Rinelli, Marc Van Barel +2
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an i…
On computing the zeros of a class of Sobolev orthogonal polynomials
Nicola Mastronardi, Marc Van Barel, Raf Vandebril +1
A fast and weakly stable method for computing the zeros of a particular class of hypergeometric polynomials is presented. The studied hypergeometric polynomials satisfy a higher or…
A free parameter depending family of polynomial wavelets on a compact interval
Woula Themistoclakis, Marc Van Barel
On a compact interval, we introduce and study a whole family of wavelets depending on a free parameter that can be suitably modulated to improve performance. Such wavelets arise fr…
A Parametric Family of Polynomial Wavelets for Signal and Image Processing
Mariantonia Cotronei, Woula Themistoclakis, Marc Van Barel
This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vallée Poussin (VP) interpola…
Adaptive cross approximation for Tikhonov regularization in general form
Thomas Mach, Lothar Reichel, Marc Van Barel
Many problems in Science and Engineering give rise to linear integral equations of the first kind with a smooth kernel. Discretization of the integral operator yields a matrix, who…
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
Simon Telen, Marc Van Barel, Jan Verschelde
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on powe…
Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder
Francoise Tisseur, Marc Van Barel
A new measure called min-max elementwise backward error is introduced for approximate roots of scalar polynomials . Compared with the elementwise relative backward error, thi…
A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation
Simon Telen, Marc Van Barel, Jan Verschelde
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and i…
Biorthogonal Extended Krylov Subspace Methods
Niel Van Buggenhout, Marc Van Barel, Raf Vandebril
A general framework for oblique projections of nonhermitian matrices onto rational Krylov subspaces is developed. To obtain this framework we revisit the classical rational Krylov…
Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras
Simon Telen, Bernard Mourrain, Marc Van Barel
We consider the problem of finding the isolated 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 ge…