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Avoiding singularities during homotopy continuation

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dc.contributor.authorHodges, Timothy E., author
dc.contributor.authorBates, Daniel J., advisor
dc.contributor.authorBöhm, A. P., committee member
dc.contributor.authorHulpke, Alexander, committee member
dc.contributor.authorPeterson, Christopher, committee member
dc.date.accessioned2017-06-09T15:42:46Z
dc.date.available2017-06-09T15:42:46Z
dc.date.issued2017
dc.description.abstractIn numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1,x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ill-conditioning. These areas can cause failure of homotopy continuation or an increase in run time. In this thesis, we formalize where these areas of ill-conditioning can happen, and give a novel method for avoiding them. In addition, future work and possible improvements to the method are proposed. We also report on related developments in the Bertini software package. In addition, we discuss new infrastructure and heuristics for tuning configurations during homotopy continuation.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierHodges_colostate_0053A_14125.pdf
dc.identifier.urihttp://hdl.handle.net/10217/181397
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectbranch points
dc.subjectnumerical algebraic geometry
dc.subjectsoftware development
dc.subjecthomotopy continuation
dc.subjectBertini
dc.subjectramification points
dc.titleAvoiding singularities during homotopy continuation
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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