Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.100
Fulltext available Open Access
Title: Abstract perturbed Krylov methods
Language: English
Authors: Zemke, Jens-Peter M.  
Keywords: Abstract perturbed Krylov method;inexact Krylov method;finite precision;Hessenberg matrix;basis polynomial
Issue Date: Jul-2005
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 89
Abstract (english): 
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.
URI: http://tubdok.tub.tuhh.de/handle/11420/102
DOI: 10.15480/882.100
Institute: Mathematik E-10 
Document Type: Preprint
License: In Copyright In Copyright
Appears in Collections:Publications with fulltext

Files in This Item:
File Description SizeFormat
rep89.pdf388,7 kBAdobe PDFView/Open
Thumbnail
Show full item record

Page view(s)

640
Last Week
2
Last month
10
checked on Jun 21, 2021

Download(s)

314
checked on Jun 21, 2021

Google ScholarTM

Check

Note about this record

Cite this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.