8 citations · 34 across the 25 of their papers we have counts for
29 papers
Updating and Downdating the Recurrences of Discrete Multiple Orthogonal Polynomials on the Real Line
Amin Faghih, Marc Van Barel, Raf Vandebril
We study multiple orthogonal polynomials with orthogonality defined by multiple positive discrete measures on the real line. Focusing on type~I and type~II multiple orthogonal poly…
Fast computation of eigenvalues of periodic CMV matrices
Thomas Mach, Michele Rinelli, Raf Vandebril +1
Periodic CMV matrices are unitary matrices that can be specified by data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using…
Block Krylov subspaces and orthogonal matrix polynomials: a structural correspondence with applications to unitary matrices
Michele Rinelli, Raf Vandebril
We study the connection between block Krylov subspaces and matrix orthogonal functions. Under a no-deflation assumption, we show that polynomial block Krylov subspaces are isometri…
ParaSLRF: A High Performance Rational Filter Method for Solving Large Scale Eigenvalue Problems
Biyi Wang, Karl Meerbergen, Raf Vandebril +2
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite genera…
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…
Manifold-valued function approximation from multiple tangent spaces
Hang Wang, Raf Vandebril, Joeri Van der Veken +1
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian…
A shifted Laplace rational filter for large-scale eigenvalue problems
Biyi Wang, Karl Meerbergen, Raf Vandebril +2
We present a rational filter for computing all eigenvalues of a symmetric definite eigenvalue problem lying in an interval on the real axis. The linear systems arising from the fil…
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…
Constructing Sobolev orthonormal rational functions via an updating procedure
Amin Faghih, Marc Van Barel, Niel Van Buggenhout +1
In this paper, we generate the recursion coefficients for rational functions with prescribed poles that are orthonormal with respect to a continuous Sobolev inner product. Using a…
Algorithms for Parallel Shared-Memory Sparse Matrix-Vector Multiplication on Unstructured Matrices
Kobe Bergmans, Karl Meerbergen, Raf Vandebril
The sparse matrix-vector (SpMV) multiplication is an important computational kernel, but it is notoriously difficult to execute efficiently. This paper investigates algorithm perfo…
The RQR algorithm
Daan Camps, Thomas Mach, Raf Vandebril +1
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eige…
An Arnoldi-based approach to polynomial and rational least squares problems
Amin Faghih, Marc Van Barel, Niel Van Buggenhout +1
In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit…
Approximating maps into manifolds with lower curvature bounds
Simon Jacobsson, Raf Vandebril, Joeri van der Veken +1
Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such func…
Algorithms for Modifying Recurrence Relations of Orthogonal Polynomial and Rational Functions when Changing the Discrete Inner Product
Marc Van Barel, Niel Van Buggenhout, Raf Vandebril
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instea…
Parallel two-stage reduction to Hessenberg-triangular form
Thijs Steel, Raf Vandebril
We present a two-stage algorithm for the parallel reduction of a pencil to Hessenberg-triangular form. Traditionally, two-stage Hessenberg-triangular reduction algorithms achieve h…
A new deflation criterion for the QZ algorithm
Thijs Steel, Raf Vandebril, Julien Langou
The QZ algorithm computes the Schur form of a matrix pencil. It is an iterative algorithm and at some point, it must decide that an eigenvalue has converged and move on with anothe…
The seriation problem in the presence of a double Fiedler value
Anna Concas, Caterina Fenu, Giuseppe Rodriguez +1
Seriation is a problem consisting of seeking the best enumeration order of a set of units whose interrelationship is described by a bipartite graph, that is, a graph whose nodes ar…
Generation of orthogonal rational functions by procedures for structured matrices
Niel Van Buggenhout, Marc Van Barel, Raf Vandebril
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 probl…
Structured backward errors in linearizations
Vanni Noferini, Leonardo Robol, Raf Vandebril
A standard approach to compute the roots of a univariate polynomial is to compute the eigenvalues of an associated \emph{confederate} matrix instead, such as, for instance the comp…
Pole-swapping algorithms for alternating and palindromic eigenvalue problems
Thomas Mach, Thijs Steel, Raf Vandebril +1
Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic a…
On pole-swapping algorithms for the eigenvalue problem
Daan Camps, Thomas Mach, Raf Vandebril +1
Pole-swapping algorithms, which are generalizations of the QZ algorithm for the generalized eigenvalue problem, are studied. A new modular (and therefore more flexible) convergence…
A multishift, multipole rational QZ method with aggressive early deflation
Thijs Steel, Daan Camps, Karl Meerbergen +1
The rational QZ method generalizes the QZ method by implicitly supporting rational subspace iteration. In this paper we extend the rational QZ method by introducing shifts and pole…
When is a matrix unitary or Hermitian plus low rank?
Gianna M. Del Corso, Federico Poloni, Leonardo Robol +1
Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing com plexity…
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…