{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/44561"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/44561","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems","abstract":"A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner.","abstract_html":"A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner.","abstract_has_math":false,"creators":["McQuain, William D."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Computer Science and Applications","degree_department":"Computer Science and Applications","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1992,"date_issued":"1992","date_published":"1992","updated_at":"2026-07-22T22:19:54Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-09052009-040457"],"render_values":[{"text":"etd-09052009-040457","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/44561","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Computer Science and Applications"]},{"key":"dc:creator","label":"Author","values":["McQuain, William D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:44:33Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:44:33Z","2009-09-05"]},{"key":"dc:date.issued","label":"Date","values":["1992"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science and Applications"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-09052009-040457"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/44561"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems"]}]}],"canonical_facts":{"dc:contributor.department":["Computer Science and Applications"],"dc:creator":["McQuain, William D."],"dc:date.accessioned":["2014-03-14T21:44:33Z"],"dc:date.available":["2014-03-14T21:44:33Z","2009-09-05"],"dc:date.issued":["1992"],"dc:description.abstract":["A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-09052009-040457"],"dc:identifier.uri":["http://hdl.handle.net/10919/44561"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Preconditioned iterative methods for highly sparse, nonsymmetric, unstructured linear algebra problems"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Computer Science and Applications"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:54Z"}