Roel Van Beeumen
Katholieke Universiteit Leuven
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Publication
Featured researches published by Roel Van Beeumen.
SIAM Journal on Scientific Computing | 2013
Roel Van Beeumen; Karl Meerbergen; Wim Michiels
This paper proposes a new rational Krylov method for solving the nonlinear eigenvalue problem:
SIAM Journal on Scientific Computing | 2014
Stefan Güttel; Roel Van Beeumen; Karl Meerbergen; Wim Michiels
A(lambda)x = 0
SIAM Journal on Matrix Analysis and Applications | 2015
Roel Van Beeumen; Karl Meerbergen; Wim Michiels
. The method approximates
Numerical Linear Algebra With Applications | 2016
Roel Van Beeumen; Elias Jarlebring; Wim Michiels
A(lambda)
ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010 | 2010
Roel Van Beeumen; Karl Meerbergen
by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue problem (GEP). To this GEP we apply a rational Krylov method that preserves the structure. The companion form grows in each iteration and the interpolation points are dynamically chosen. Each iteration requires a linear system solve with
Ima Journal of Numerical Analysis | 2015
Roel Van Beeumen; Wim Michiels; Karl Meerbergen
A(sigma)
Journal of Computational Electronics | 2014
William G. Vandenberghe; Massimo V. Fischetti; Roel Van Beeumen; Karl Meerbergen; Wim Michiels; Cedric Effenberger
, where
Ima Journal of Numerical Analysis | 2017
Karl Meerbergen; Emre Mengi; Wim Michiels; Roel Van Beeumen
sigma
Archive | 2014
Roel Van Beeumen; Karl Meerbergen; Wim Michiels
is the last interpolation point. The method is illustrated by small- and large-scale numerical examples. In particular, we illustrate that the method is fully dynamic and can be used as a global search method as well as a local refinement method. In the last case, we compare the method to Newtons method and illustrate that we can achieve an even faster convergence rate.
International Journal of Dynamics and Control | 2014
Dries Verhees; Roel Van Beeumen; Karl Meerbergen; Nicola Guglielmi; Wim Michiels
A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems is proposed. This iterative method, called fully rational Krylov method for nonlinear eigenvalue problems (abbreviated as NLEIGS), is based on linear rational interpolation and generalizes the Newton rational Krylov method proposed in [R. Van Beeumen, K. Meerbergen, and W. Michiels, SIAM J. Sci. Comput., 35 (2013), pp. A327-A350]. NLEIGS utilizes a dynamically constructed rational interpolant of the nonlinear operator and a new companion-type linearization for obtaining a generalized eigenvalue problem with special structure. This structure is particularly suited for the rational Krylov method. A new approach for the computation of rational divided differences using matrix functions is presented. It is shown that NLEIGS has a computational cost comparable to the Newton rational Krylov method but converges more reliably, in particular, if the nonlinear operator has singularities nearby the target set. Moreover, NLEIGS implements an automatic scaling procedure which makes it work robustly independent of the location and shape of the target set, and it also features low-rank approximation techniques for increased computational efficiency. Small- and large-scale numerical examples are included.