Abstract perturbed Krylov methods

Publikationstyp
Preprint
Publikationsdatum
2005-07
Sprache
English
Author
Zemke, Jens-Peter M. orcid-logo
Institut
Mathematik E-10 
DOI
10.15480/882.100
TORE-URI
http://tubdok.tub.tuhh.de/handle/11420/102
Lizenz
http://rightsstatements.org/vocab/InC/1.0/
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.
Schlagworte
Abstract perturbed Krylov method
inexact Krylov method
finite precision
Hessenberg matrix
basis polynomial
DDC Class
510: Mathematik