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On Structured Pencils arising in Sonneveld Methods
Citation Link: https://doi.org/10.15480/882.1180
Publikationstyp
Preprint
Date Issued
2014-07
Sprache
English
Author(s)
Institut
TORE-DOI
First published in
Preprints des Institutes für Mathematik;Bericht 186
Number in series
186
The pencils arising in Sonneveld methods, e.g., methods based on the induced dimension reduction (IDR) principle by Sonneveld and van Gijzen, are highly structured and some eigenvalues are known. The other eigenvalues are approximations to eigenvalues of the matrix used to compute the Sonneveld pencil. In [SIAM J. Matrix Anal. Appl. 34(2), 2013, pp. 283–311] we proved that it is possible to purify the characteristic polynomial from the known values by moving them to infinity and to deflate the problem to obtain a smaller pencil that has only the other eigenvalues. Depending on the strategy used to select the known eigenvalues, this may result in large condition numbers or even break down due to a singular pencil. In this paper we prove that there are one-dimensional families of purified and deflated pencils that all have the same eigenvalues. We give a selection scheme to chose a pencil suitable for the stable computation of the wanted eigenvalues.
Subjects
Krylovraumverfahren
Sonneveldmethoden
strukturierte Büschel
Krylov subspace method
Sonneveld methods
structured pencils
eigenvalues
DDC Class
510: Mathematik
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