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  4. Abstract perturbed Krylov methods
 
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Abstract perturbed Krylov methods

Citation Link: https://doi.org/10.15480/882.100
Publikationstyp
Preprint
Date Issued
2005-07
Sprache
English
Author(s)
Zemke, Jens-Peter M.  orcid-logo
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.100
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/102
First published in
Preprints des Institutes für Mathematik  
Preprints des Institutes für Mathematik:Bericht 89
Number in series
89
We introduce the framework of abstract perturbed Krylov methods''. This is a new and unifying point of view on Krylov subspace methods based solely on the matrix equation $AQ_k+F_k=Q_{k+1}underline{C}_k=Q_kC_k+q_{k+1}c_{k+1,k}e_k^T$ and the assumption that the matrix $C_k$ is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, (Q)OR iterates and (Q)MR iterates to the starting vector $q_1$ and the perturbation terms ${f_l}_{l=1}^k$. The properties of these polynomials and similarities between them are analyzed in some detail. The results suggest the interpretation of abstract perturbed Krylov methods as additive overlay of several abstract exact Krylov methods.
Subjects
Abstract perturbed Krylov method
inexact Krylov method
finite precision
Hessenberg matrix
basis polynomial
DDC Class
510: Mathematik
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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