Abstract perturbed Krylov methods Export

@article{citeulike:1410550, abstract = {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 and the assumption that the matrix Ck is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, quasi-orthogonal residual iterates and quasi-minimal residual iterates to the starting vector q1 and the perturbation term Fk. 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.}, author = {Zemke, Jens-Peter M.}, citeulike-article-id = {1410550}, citeulike-linkout-0 = {http://www.sciencedirect.com/science/article/B6V0R-4N3P0CW-1/2/f516978bcc5003954e6e4fd8c5c5b250}, day = {15}, journal = {Linear Algebra and its Applications}, keywords = {invariant, krylov, subspace}, month = {July}, number = {2-3}, pages = {405--434}, posted-at = {2007-06-25 13:09:34}, priority = {4}, title = {Abstract perturbed Krylov methods}, url = {http://www.sciencedirect.com/science/article/B6V0R-4N3P0CW-1/2/f516978bcc5003954e6e4fd8c5c5b250}, volume = {424}, year = {2007} }

TY - JOUR ID - citeulike:1410550 L3 - citeulike-article-id:1410550 N2 - 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 and the assumption that the matrix Ck is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, quasi-orthogonal residual iterates and quasi-minimal residual iterates to the starting vector q1 and the perturbation term Fk. 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. IS - 2-3 JF - Linear Algebra and its Applications EP - 434 TI - Abstract perturbed Krylov methods VL - 424 SP - 405 KW - invariant KW - krylov KW - subspace AU - Zemke, Jens-Peter PY - 2007/07/15/ UR - http://www.sciencedirect.com/science/article/B6V0R-4N3P0CW-1/2/f516978bcc5003954e6e4fd8c5c5b250 ER -