{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/90914"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/90914","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"An augmented Jacobian matrix algorithm for tracking homotopy zero curves","abstract":"There are algorithms for finding zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices.","abstract_html":"There are algorithms for finding zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. 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The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.S."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["An augmented Jacobian matrix algorithm for tracking homotopy zero curves"]}]}],"canonical_facts":{"dc:contributor.department":["Computer Science and Applications"],"dc:creator":["Billups, Stephen C."],"dc:date.accessioned":["2019-07-03T16:42:32Z"],"dc:date.available":["2019-07-03T16:42:32Z"],"dc:date.issued":["1985"],"dc:description.abstract":["There are algorithms for finding zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. 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The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices."],"dc:description.degree":["M.S."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/90914"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["An augmented Jacobian matrix algorithm for tracking homotopy zero curves"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Computer Science and Applications"],"thesis:degree_level":["masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:01Z"}