{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/34765"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/34765","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB","abstract":"Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results.","abstract_html":"Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. 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This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. Augmented bi-Lanczos algorithm and modified two-term recurrence are developed for using the recycle space. Recycle space is built from the approximate invariant subspace corresponding to eigenvalues close to the origin. Recycling approach is extended to the CGS and the BiCGSTAB algorithms. Experiments on a convection-diffusion problem give promising results."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB"]}]}],"canonical_facts":{"dc:contributor.committeechair":["de Sturler, Eric"],"dc:contributor.committeemember":["Gugercin, Serkan","Borggaard, Jeffrey T.","Beattie, Christopher A."],"dc:contributor.department":["Mathematics"],"dc:creator":["Ahuja, Kapil"],"dc:date.accessioned":["2014-03-14T20:44:11Z"],"dc:date.available":["2014-03-14T20:44:11Z","2009-09-21"],"dc:date.issued":["2009-08-13"],"dc:description.abstract":["Engineering problems frequently require solving a sequence of dual linear systems. This paper introduces recycling BiCG, that recycles the Krylov subspace from one pair of linear systems to the next pair. 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Experiments on a convection-diffusion problem give promising results."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-08252009-161256"],"dc:identifier.uri":["http://hdl.handle.net/10919/34765"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Krylov subspace recycling","Petrov-Galerkin formulation","bi-Lanczos method"],"dc:title":["Recycling Bi-Lanczos Algorithms: BiCG, CGS, and BiCGSTAB"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:38Z"}