Title: On the convergence of rational Ritz-values
Authors: Beckermann, Bernd * ×
Güttel, Stefan *
Vandebril, Raf * #
Issue Date: Mar-2010
Publisher: Society for Industrial and Applied Mathematics
Series Title: SIAM Journal on Matrix Analysis and Applications vol:31 issue:4 pages:1740-1774
Abstract: Ruhe's rational Krylov method is a popular tool for approximating eigenvalues of a given matrix, though its convergence behavior is far from being fully understood. Under fairly general assumptions we characterize in an asymptotic sense which eigenvalues of a Hermitian matrix are approximated by rational Ritz values and how fast this approximation takes place. Our main tool is a constrained extremal problem from logarithmic potential theory, where an additional external field is required for taking into account the poles of the underlying rational Krylov space. Several examples illustrate our analytic results.
ISSN: 0895-4798
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
* (joint) first author
× corresponding author
# (joint) last author

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