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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
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.
DOI: 10.15480/882.100
Institute: Mathematik E-10 
Document Type: Preprint
License: In Copyright In Copyright
Part of Series: Preprints des Institutes für Mathematik 
Volume number: 89
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