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Gale duality, decoupling, parameter homotopies, and monodromy

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dc.contributor.authorNiemerg, Matthew E., author
dc.contributor.authorBates, Daniel J., advisor
dc.contributor.authorShipman, Patrick, committee member
dc.contributor.authorPeterson, Christopher, committee member
dc.contributor.authorLee, Chihoon, committee member
dc.date.accessioned2007-01-03T06:40:46Z
dc.date.available2007-01-03T06:40:46Z
dc.date.issued2014
dc.description.abstractNumerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierNiemerg_colostate_0053A_12232.pdf
dc.identifier.urihttp://hdl.handle.net/10217/82567
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.subjectgale duality
dc.subjectparameter homotopies
dc.subjectnumerical algebraic geometry
dc.subjectmonodromy
dc.titleGale duality, decoupling, parameter homotopies, and monodromy
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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