15 citations · 47 across the 25 of their papers we have counts for
25 papers · 1 filter
Compact Rational Krylov for Parametrized Systems with Application to BEM Frequency Sweeping
Kobe Bruyninckx, Daan Huybrechs, Karl Meerbergen
In parametrized linear systems the system matrix depends nonlinearly on a parameter and solutions are sought for many values o…
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…
Linearizing a nonlinear eigenvalue problem with quadratic rational eigenvector nonlinearities
Victor Janssens, Karl Meerbergen, Wim Michiels
Nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv) are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from computationa…
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…
Efficient parallel inversion of ParaOpt preconditioners
Corentin Bonte, Arne Bouillon, Giovanni Samaey +1
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a sy…
The shift-and-invert Arnoldi method for singular matrix pencils
Karl Meerbergen, Zhijun Wang
A popular method for solving large sparse regular eigenvalue problem is the shift-and-invert Arnoldi method. This paper aims to use the method for large sparse singular pencils. In…
Uniform H-matrix Compression with Applications to Boundary Integral Equations
Kobe Bruyninckx, Daan Huybrechs, Karl Meerbergen
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the -matrix format, this sparsity is exploited to achieve $…
QR-based Parallel Set-Valued Approximation with Rational Functions
Simon Dirckx, Karl Meerbergen, Daan Huybrechs
In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm f…
Diagonalization-based preconditioners and generalized convergence bounds for ParaOpt
Arne Bouillon, Giovanni Samaey, Karl Meerbergen
The ParaOpt algorithm was recently introduced as a time-parallel solver for optimal-control problems with a terminal-cost objective, and convergence results have been presented for…
On generalized preconditioners for time-parallel parabolic optimal control
Arne Bouillon, Giovanni Samaey, Karl Meerbergen
The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control…
Time integration of finite element models with nonlinear frequency dependencies
Elke Deckers, Stijn Jonckheere, Karl Meerbergen
The analysis of sound and vibrations is often performed in the frequency domain, implying the assumption of steady-state behaviour and time-harmonic excitation. External excitation…
Contour Integration for Eigenvector Nonlinearities
Rob Claes, Karl Meerbergen, Simon Telen
Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonline…
Linearizability of eigenvector nonlinearities
Rob Claes, Elias Jarlebring, Karl Meerbergen +1
We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by s…
Frequency extraction for BEM-matrices arising from the 3D scalar Helmholtz equation
Simon Dirckx, Daan Huybrechs, Karl Meerbergen
The discretisation of boundary integral equations for the scalar Helmholtz equation leads to large dense linear systems. Efficient boundary element methods (BEM), such as the fast…
Subspace method for multiparameter-eigenvalue problems based on tensor-train representations
Koen Ruymbeek, Karl Meerbergen, Wim Michiels
In this paper we solve -parameter eigenvalue problems (EPs), with any natural number by representing the problem using Tensor-Trains (TT) and designing a method based on…
Tensor-Krylov method for computing eigenvalues of parameter-dependent matrices
Koen Ruymbeek, Karl Meerbergen, Wim Michiels
In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant,...) to the case where the matrices depend on parameters…
Calculating the minimal/maximal eigenvalue of symmetric parametrized matrices using projection
Koen Ruymbeek, Karl Meerbergen, Wim Michiels
In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a…
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…
Two-level preconditioning for Ridge Regression
Joris Tavernier, Jaak Simm, Karl Meerbergen +1
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the…
Automatic rational approximation and linearization of nonlinear eigenvalue problems
Pieter Lietaert, Javier Pérez, Bart Vandereycken +1
We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, Sète, and Trefethen to approximate the no…
Subspace Methods for 3-Parameter Eigenvalue Problems
Michiel E. Hochstenbach, Karl Meerbergen, Emre Mengi +1
We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular exam…
A rational QZ method
Daan Camps, Karl Meerbergen, Raf Vandebril
We propose a rational QZ method for the solution of the dense, unsymmetric generalized eigenvalue problem. This generalization of the classical QZ method operates implicitly on a H…
Mixed forward-backward stability of the two-level orthogonal Arnoldi method for quadratic problems
Karl Meerbergen, Javier Pérez
We revisit the numerical stability of the two-level orthogonal Arnoldi (TOAR) method for computing an orthonormal basis of a second--order Krylov subspace associated with two given…
A Subspace Method for Large Scale Eigenvalue Optimization
Fatih Kangal, Karl Meerbergen, Emre Mengi +1
We consider the minimization or maximization of the th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix An…