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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)
Institut
TORE-DOI
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
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