Preconditioning polynomial systems for homotopy continuation
| dc.contributor.author | Ihde, Steven L., author | |
| dc.contributor.author | Bates, Dan, advisor | |
| dc.contributor.author | Peterson, Chris, committee member | |
| dc.contributor.author | Young, Peter, committee member | |
| dc.date.accessioned | 2007-01-03T05:48:02Z | |
| dc.date.available | 2007-01-03T05:48:02Z | |
| dc.date.issued | 2011 | |
| dc.description.abstract | Polynomial systems are ubiquitous in today's scientific world. These systems need to be solved quickly and efficiently. One key solution method comes from Numerical Algebraic Geometry, specifically Homotopy Continuation. This method involves following paths from the solutions of a simpler system to the solutions of the target system. If we can follow fewer or better conditioned paths to the solution set, the result is better efficiency. Our goal is to precondition the original system in order to achieve such efficiency. Using dual spaces and H-bases, we are able to remove poorly conditioned paths and at worst replace them with, possibly more, better conditioned paths. At best we can trim the system down so that we track only the paths that lead to solutions. These techniques require only numerical linear algebra and are therefore easily computed. In this thesis we will introduce H-bases and dual spaces, show some promising preliminary results, and discuss further work in this area. | |
| dc.format.medium | born digital | |
| dc.format.medium | masters theses | |
| dc.identifier | Ihde_colostate_0053N_10543.pdf | |
| dc.identifier.uri | http://hdl.handle.net/10217/51875 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright 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.subject | dual basis | |
| dc.subject | polynomial systems | |
| dc.subject | numerical algebraic geometry | |
| dc.subject | homotopy continuation | |
| dc.subject | H-basis | |
| dc.title | Preconditioning polynomial systems for homotopy continuation | |
| dc.type | Text | |
| dcterms.rights.dpla | This 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.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.S.) |
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