IDR: A new generation of Krylov subspace methods?

Publikationstyp
Preprint
Publikationsdatum
2012-04
Sprache
English
Author
Rendel, Olaf 
Rizvanolli, Anisa 
Zemke, Jens-Peter M. orcid-logo
Institut
Mathematik E-10 
DOI
10.15480/882.1054
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/1056
First published in
Preprints des Institutes für Mathematik 
Preprints des Institutes für Mathematik;Bericht 161
Number in series
161
Citation
Preprint. Published in: Linear Algebra and its ApplicationsVolume 439, Issue 4, 15 August 2013, Pages 1040-1061
Publisher DOI
10.1016/j.laa.2012.11.021
Scopus ID
2-s2.0-84879889999
The Induced Dimension Reduction (IDR) technique developed by Sonneveld and van Gijzen is a powerful concept resulting in a variety of transpose-free Krylov subspace methods based on short-term recurrences. We present the main differences between and similarities of IDR methods and classical Krylov subspace methods; our tool of trade is the so-called generalized Hessenberg decomposition. The concept of ''transfer'' of techniques from the setting of (classical) Krylov subspace methods to the IDR based methods is introduced. For simplicity, we only sketch some recent results in the fields of eigenvalue computations and of solution of linear systems.
Schlagworte
Induzierte Dimensions-Reduktion
Krylov-Unterraum-Verfahren
Transponierten-freies Verfahren
Iteratives Verfahren
Eigenwertberechnung
Induced dimension reduction
Krylov subspace method
transpose-free method
iterative method
eigenvalue computation
DDC Class
510: Mathematik
Lizenz
http://doku.b.tu-harburg.de/doku/lic_mit_pod.php
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