{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99410"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99410","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides","abstract":"Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior solutions. We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.","abstract_html":"Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior solutions. We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.","abstract_has_math":false,"creators":["Christensen, Nicholas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Fischer, Paul F."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:49:11Z","date_published":"2018-03-13T15:49:11Z","updated_at":"2026-07-22T22:24:37Z","subjects":["Iterative solver","Projection","Solution approximation","Ax = b","Partial differential equations","Linear system","Oblique inner product","Oblique QR factorization","Updating QR factorization","Successive right hand side","Initial guess","Reduced communication"],"languages":["en"],"rights":["This thesis is released into the public domain under the CC0 code. To the extent possible under law, the author waives all copyright and related or neighboring rights to this work.","Copyright 2017 Nicholas Christensen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99410","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fischer, Paul F."]},{"key":"dc:creator","label":"Author","values":["Christensen, Nicholas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:49:11Z","2017-12-11","2017-12"]},{"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":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["Iterative solver","Projection","Solution approximation","Ax = b","Partial differential equations","Linear system","Oblique inner product","Oblique QR factorization","Updating QR factorization","Successive right hand side","Initial guess","Reduced communication"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["This thesis is released into the public domain under the CC0 code. To the extent possible under law, the author waives all copyright and related or neighboring rights to this work.","Copyright 2017 Nicholas Christensen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99410"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Accurate initial guesses to the solution can dramatically speed convergence of iterative solvers. In the case of successive right hand sides, it has been shown that accurate initial solutions may be obtained by projecting the newest right hand side vector onto a column space of recent prior solutions. We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Nicholas Christensen, accepted the attached license on 2017-12-08 at 16:59.","The student, Nicholas Christensen, submitted this Thesis for approval on 2017-12-08 at 17:39.","This Thesis was approved for publication on 2017-12-11 at 15:33.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11931 on 2018-03-13 at 10:12:00","Made available in DSpace on 2018-03-13T15:49:11Z (GMT). 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We propose a technique to efficiently update the column space of prior solutions. We find this technique can modestly improve solver performance, though its potential is likely limited by the problem step size and the accuracy of the solver.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Nicholas Christensen, accepted the attached license on 2017-12-08 at 16:59.","The student, Nicholas Christensen, submitted this Thesis for approval on 2017-12-08 at 17:39.","This Thesis was approved for publication on 2017-12-11 at 15:33.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11931 on 2018-03-13 at 10:12:00","Made available in DSpace on 2018-03-13T15:49:11Z (GMT). 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To the extent possible under law, the author waives all copyright and related or neighboring rights to this work.","Copyright 2017 Nicholas Christensen"],"dc:subject":["Iterative solver","Projection","Solution approximation","Ax = b","Partial differential equations","Linear system","Oblique inner product","Oblique QR factorization","Updating QR factorization","Successive right hand side","Initial guess","Reduced communication"],"dc:title":["Efficient projection space updates for the approximation of iterative solutions to linear systems with successive right hand sides"],"dc:type":["text"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:37Z"}