9 papers
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…
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…
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…
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 $…
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…