{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/81615"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/81615","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Three Dimensional Pseudospectral Self -Consistent Field Approximation","abstract":"For the eigenvalue problem, a novel variant of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is transformed back to the original space. In Arnoldi's method, vectors in the selected range of the energy spectrum are amplified by a specially designed energy range selector, which amounts to tempered inverse iteration. The starting vectors for Arnoldi are enriched with new randomized components in order to decrease the iteration number and to reduce the chance of missing eigenvectors. The linear systems in the Krylov space generation are solved by a spectrally preconditioned conjugate gradient (CG) method. The energy range selector contains two parameters, which let us select a limited range in the eigenvalue spectrum. With the greatly improved adaptive algorithm for controlling the parameters and the more flexible adjustable subspace size, the solver has become highly efficient, robust and accurate.","abstract_html":"For the eigenvalue problem, a novel variant of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is transformed back to the original space. In Arnoldi's method, vectors in the selected range of the energy spectrum are amplified by a specially designed energy range selector, which amounts to tempered inverse iteration. The starting vectors for Arnoldi are enriched with new randomized components in order to decrease the iteration number and to reduce the chance of missing eigenvectors. The linear systems in the Krylov space generation are solved by a spectrally preconditioned conjugate gradient (CG) method. The energy range selector contains two parameters, which let us select a limited range in the eigenvalue spectrum. With the greatly improved adaptive algorithm for controlling the parameters and the more flexible adjustable subspace size, the solver has become highly efficient, robust and accurate.","abstract_has_math":false,"creators":["Chow, Wing Fai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Kerkhoven, Thomas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:19:32Z","date_published":"2015-09-25T20:19:32Z","updated_at":"2026-07-22T22:26:16Z","subjects":["Computer Science"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3086035"],"render_values":[{"text":"(MiAaPQ)AAI3086035","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/81615","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kerkhoven, Thomas"]},{"key":"dc:creator","label":"Author","values":["Chow, Wing Fai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:19:32Z","10000-01-01","2003"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/81615","(MiAaPQ)AAI3086035"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["For the eigenvalue problem, a novel variant of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is transformed back to the original space. In Arnoldi's method, vectors in the selected range of the energy spectrum are amplified by a specially designed energy range selector, which amounts to tempered inverse iteration. The starting vectors for Arnoldi are enriched with new randomized components in order to decrease the iteration number and to reduce the chance of missing eigenvectors. The linear systems in the Krylov space generation are solved by a spectrally preconditioned conjugate gradient (CG) method. The energy range selector contains two parameters, which let us select a limited range in the eigenvalue spectrum. With the greatly improved adaptive algorithm for controlling the parameters and the more flexible adjustable subspace size, the solver has become highly efficient, robust and accurate.","Made available in DSpace on 2015-09-25T20:19:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086035.pdf: 4072373 bytes, checksum: 1ab6d97b4b91529ea42b57e3a326f2f5 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 82896 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","94 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."]},{"key":"dc:title","label":"Title","values":["Three Dimensional Pseudospectral Self -Consistent Field Approximation"]}]}],"canonical_facts":{"dc:contributor":["Kerkhoven, Thomas"],"dc:creator":["Chow, Wing Fai"],"dc:date":["2015-09-25T20:19:32Z","10000-01-01","2003"],"dc:description":["For the eigenvalue problem, a novel variant of Davidson's method, or spectrally localized Arnoldi's method, is used. The full-size problem is projected onto Krylov subspaces of limited size with an explicitly orthogonalized basis. The smaller-size projected problem is solved using LAPACK library functions and then the solution is transformed back to the original space. In Arnoldi's method, vectors in the selected range of the energy spectrum are amplified by a specially designed energy range selector, which amounts to tempered inverse iteration. The starting vectors for Arnoldi are enriched with new randomized components in order to decrease the iteration number and to reduce the chance of missing eigenvectors. The linear systems in the Krylov space generation are solved by a spectrally preconditioned conjugate gradient (CG) method. The energy range selector contains two parameters, which let us select a limited range in the eigenvalue spectrum. With the greatly improved adaptive algorithm for controlling the parameters and the more flexible adjustable subspace size, the solver has become highly efficient, robust and accurate.","Made available in DSpace on 2015-09-25T20:19:32Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086035.pdf: 4072373 bytes, checksum: 1ab6d97b4b91529ea42b57e3a326f2f5 (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 82896 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","94 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."],"dc:identifier":["http://hdl.handle.net/2142/81615","(MiAaPQ)AAI3086035"],"dc:language":["eng"],"dc:subject":["Computer Science"],"dc:title":["Three Dimensional Pseudospectral Self -Consistent Field Approximation"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:16Z"}