Zemke, Jens-Peter M.Jens-Peter M.Zemke2006-02-012006-02-012005-07http://tubdok.tub.tuhh.de/handle/11420/102We 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.enhttp://rightsstatements.org/vocab/InC/1.0/Abstract perturbed Krylov methodinexact Krylov methodfinite precisionHessenberg matrixbasis polynomialMathematikPreprint2006-02-01urn:nbn:de:gbv:830-opus-158710.15480/882.100Krylov-VerfahrenOverdetermined systems, pseudoinversesEigenvalues, eigenvectorsDeterminants, permanents, other special matrix functionsIterative methods for linear systemsMatrix equations and identitiesComplexity and performance of numerical algorithms11420/10210.15480/882.100930767805Other