{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/49413"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/49413","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the problem of parallelizing manifold covering algorithms","abstract":"Continuation methods are numerical algorithms used to determine the solution space of systems of nonlinear equations with associated sets of parameters. Such methods have been very successful in computing solution manifolds of dimension one. For higher dimensional manifolds, different techniques have been tried, with one method, Henderson's Algorithm, offering the most promise. However, the enormous size of the systems encountered in practice, along with the high dimensionality of the solution manifold, may make the method too slow for practical use. This thesis evaluates an approach for the parallel computation of manifolds. We experiment with a few variations before deciding on an approach that proves most promising. We use the COCO toolbox, written in MATLAB, for all our experiments. In particular, we make use of MATLAB's Parallel Computing Toolbox, which provides the infrastructure for limited parallel processing. In the course of our work, we discuss various issues faced when computing manifolds in parallel, such as the efficient merging of manifolds and accurate estimates of performance improvement over corresponding serial methods. In the concluding chapters, we show some results that were obtained using our implementation and discuss improvements that might make the algorithm even more efficient.","abstract_html":"Continuation methods are numerical algorithms used to determine the solution space of systems of nonlinear equations with associated sets of parameters. Such methods have been very successful in computing solution manifolds of dimension one. For higher dimensional manifolds, different techniques have been tried, with one method, Henderson's Algorithm, offering the most promise. However, the enormous size of the systems encountered in practice, along with the high dimensionality of the solution manifold, may make the method too slow for practical use. This thesis evaluates an approach for the parallel computation of manifolds. We experiment with a few variations before deciding on an approach that proves most promising. We use the COCO toolbox, written in MATLAB, for all our experiments. In particular, we make use of MATLAB's Parallel Computing Toolbox, which provides the infrastructure for limited parallel processing. In the course of our work, we discuss various issues faced when computing manifolds in parallel, such as the efficient merging of manifolds and accurate estimates of performance improvement over corresponding serial methods. In the concluding chapters, we show some results that were obtained using our implementation and discuss improvements that might make the algorithm even more efficient.","abstract_has_math":false,"creators":["Mallya, Pratik"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Dankowicz, Harry"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-30T16:42:42Z","date_published":"2014-05-30T16:42:42Z","updated_at":"2026-07-22T22:25:38Z","subjects":["Numerical Continuation","Atlas Algorithms","Higher Dimensional Manifolds"],"languages":["en"],"rights":["Copyright 2014 Pratik Mallya"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/49413","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dankowicz, Harry"]},{"key":"dc:creator","label":"Author","values":["Mallya, Pratik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-05-30T16:42:42Z","2014-05"]},{"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":["Numerical Continuation","Atlas Algorithms","Higher Dimensional Manifolds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Pratik Mallya"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/49413"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Continuation methods are numerical algorithms used to determine the solution space of systems of nonlinear equations with associated sets of parameters. 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However, the enormous size of the systems encountered in practice, along with the high dimensionality of the solution manifold, may make the method too slow for practical use. This thesis evaluates an approach for the parallel computation of manifolds. We experiment with a few variations before deciding on an approach that proves most promising. We use the COCO toolbox, written in MATLAB, for all our experiments. In particular, we make use of MATLAB's Parallel Computing Toolbox, which provides the infrastructure for limited parallel processing. In the course of our work, we discuss various issues faced when computing manifolds in parallel, such as the efficient merging of manifolds and accurate estimates of performance improvement over corresponding serial methods. 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