{"id":{"repo_id":"baylor","oai_identifier":"oai:baylor-ir.tdl.org:2104/5219"},"canonical_url":"https://search.dev.ndltd.org/etd/baylor/oai:baylor-ir.tdl.org:2104/5219","repository":{"repo_id":"baylor","name":"Baylor University","base_url":"https://baylor-ir.tdl.org/server/oai/request"},"display":{"title":"Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.","abstract":"We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos.","abstract_html":"We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos.","abstract_has_math":false,"creators":["Nicely, Dywayne A."],"institution":"Baylor University.","degree_name":"Ph.D.","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Morgan, Ronald Benjamin, 1958-"],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-10","date_published":"2008-10","updated_at":"2026-07-24T01:08:04Z","subjects":["Eigenvalues.","Algorithms.","Eigenvectors.","Linear systems.","Iterative methods (Mathematics)","Orthogonalization methods."],"languages":["en"],"rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2104/5219","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Morgan, Ronald Benjamin, 1958-"]},{"key":"dc:creator","label":"Author","values":["Nicely, Dywayne A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2008-10-02T18:39:19Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2008-10-02T18:39:19Z"]},{"key":"dc:date.issued","label":"Date","values":["2008-10"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Baylor University."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Eigenvalues.","Algorithms.","Eigenvectors.","Linear systems.","Iterative methods (Mathematics)","Orthogonalization methods."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2104/5219"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Restarting the Lanczos algorithm for large eigenvalue problems and linear equations."]}]}],"canonical_facts":{"dc:contributor.advisor":["Morgan, Ronald Benjamin, 1958-"],"dc:creator":["Nicely, Dywayne A."],"dc:date.accessioned":["2008-10-02T18:39:19Z"],"dc:date.available":["2008-10-02T18:39:19Z"],"dc:date.issued":["2008-10"],"dc:description.abstract":["We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For the symmetric case, we give a method called Lan-DR that simultaneously solves linear equations and computes eigenvalues and eigenvectors. The use of approximate eigenvectors deflates eigenvalues. Maintaining the orthogonality of the Lanczos vectors is a concern. We suggest an approach that is a combination of Parlett and Scott's idea of selective orthogonalization and Simon's partial orthogonalization. For linear systems with multiple right-sides, eigenvectors computed during the solution of the first right-hand side can be used to give much faster convergence of the second and subsequent right-hand sides. A restarted version of the nonsymmetric Lanczos algorithm is developed. Both the right and left eigenvectors are computed while systems of linear equations are solved. We also investigate a restarted two-sided Arnoldi. We compare expense and stability of this approach with restarted nonsymmetric Lanczos."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/2104/5219"],"dc:language.iso":["en"],"dc:rights":["Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission."],"dc:subject":["Eigenvalues.","Algorithms.","Eigenvectors.","Linear systems.","Iterative methods (Mathematics)","Orthogonalization methods."],"dc:title":["Restarting the Lanczos algorithm for large eigenvalue problems and linear equations."],"dc:type":["Thesis"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["Baylor University."]},"updated_at":"2026-07-24T01:08:04Z"}