{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69560"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69560","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Solution of Nonsymmetric Systems of Equations on a Multiprocessor","abstract":"We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two and three space dimensions. Specifically, we focus our attention on non-symmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors.","abstract_html":"We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two and three space dimensions. Specifically, we focus our attention on non-symmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors.","abstract_has_math":false,"creators":["Kamath, Chandrika"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:25:48Z","date_published":"2014-12-15T19:25:48Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Computer Science"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8701521"],"render_values":[{"text":"(UMI)AAI8701521","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69560","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kamath, Chandrika"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:25:48Z","10000-01-01","1986"]},{"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":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69560","(UMI)AAI8701521"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two and three space dimensions. Specifically, we focus our attention on non-symmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors.","In the first part of the thesis, we study the numerical properties of the algorithm and compare its performance with other algorithms such as the conjugate gradient method on the normal equations, the Chebyshev method, Orthomin(k), GCR(k) and GMRES(k). We also study the effect of various preconditioners on these methods. In the second part of the thesis, we implement our algorithm on the CRAY X-MP/48 multiprocessor and study its behavior as the number of processors is increased.","Made available in DSpace on 2014-12-15T19:25:48Z (GMT). No. of bitstreams: 1 8701521.pdf: 5190877 bytes, checksum: a544bf63059545b5419d379da88f832f (MD5) Previous issue date: 1986","Embargo set by: Seth Robbins for item 69726 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","185 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986."]},{"key":"dc:title","label":"Title","values":["Solution of Nonsymmetric Systems of Equations on a Multiprocessor"]}]}],"canonical_facts":{"dc:creator":["Kamath, Chandrika"],"dc:date":["2014-12-15T19:25:48Z","10000-01-01","1986"],"dc:description":["We consider the iterative solution of large sparse linear systems of equations arising from elliptic and parabolic partial differential equations in two and three space dimensions. Specifically, we focus our attention on non-symmetric systems of equations whose eigenvalues lie on both sides of the imaginary axis, or whose symmetric part is not positive definite. This system of equations is solved using the projection methods with conjugate gradient acceleration. The algorithm has been designed with special emphasis on its suitability for multiprocessors.","In the first part of the thesis, we study the numerical properties of the algorithm and compare its performance with other algorithms such as the conjugate gradient method on the normal equations, the Chebyshev method, Orthomin(k), GCR(k) and GMRES(k). We also study the effect of various preconditioners on these methods. In the second part of the thesis, we implement our algorithm on the CRAY X-MP/48 multiprocessor and study its behavior as the number of processors is increased.","Made available in DSpace on 2014-12-15T19:25:48Z (GMT). No. of bitstreams: 1 8701521.pdf: 5190877 bytes, checksum: a544bf63059545b5419d379da88f832f (MD5) Previous issue date: 1986","Embargo set by: Seth Robbins for item 69726 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","185 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986."],"dc:identifier":["http://hdl.handle.net/2142/69560","(UMI)AAI8701521"],"dc:subject":["Computer Science"],"dc:title":["Solution of Nonsymmetric Systems of Equations on a Multiprocessor"],"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":"2026-07-22T22:26:01Z"}