The Levenberg-Marquardt Method and its Implementation in Python
| dc.contributor.author | Kaltenbach, Marius | |
| dc.date.accessioned | 2023-01-09T09:38:03Z | |
| dc.date.available | 2023-01-09T09:38:03Z | |
| dc.date.issued | 2022 | eng |
| dc.description.abstract | The Levenberg-Marquardt method is a widely used algorithm applied to solve nonlinear least-squares problems. In this thesis, the Levenberg-Marquardt method is implemented in Python as a trust-region approach based on the works of Moré [Mor78] and Nocedal and Wright [NW06]. After a detailed description of the method, the Python code is presented. The Levenberg-Marquardt method is then tested on seven least-squares problems, including small-residual and large-residual problems as well as a poorly scaled one. In particular, the combination of large residuals and poor scaling makes the method slow, as it needs a large number of iterations to converge. Afterwards, the test results are compared to line search methods, such as the Gauss-Newton method. Regarding the test problems, the Levenberg-Marquardt method performed as the most robust algorithm. | eng |
| dc.description.version | published | eng |
| dc.identifier.ppn | 1830553011 | |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/59650 | |
| dc.language.iso | eng | eng |
| dc.rights | terms-of-use | |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | |
| dc.subject.ddc | 510 | eng |
| dc.subject.msc | Numerical Optimization | |
| dc.title | The Levenberg-Marquardt Method and its Implementation in Python | eng |
| dc.type | MSC_THESIS | eng |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @mastersthesis{Kaltenbach2022Leven-59650,
year={2022},
title={The Levenberg-Marquardt Method and its Implementation in Python},
address={Konstanz},
school={Universität Konstanz},
author={Kaltenbach, Marius}
} | |
| kops.citation.iso690 | KALTENBACH, Marius, 2022. The Levenberg-Marquardt Method and its Implementation in Python [Master thesis]. Konstanz: Universität Konstanz | deu |
| kops.citation.iso690 | KALTENBACH, Marius, 2022. The Levenberg-Marquardt Method and its Implementation in Python [Master thesis]. Konstanz: Universität Konstanz | eng |
| kops.citation.rdf | <rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/59650">
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-01-09T09:38:03Z</dcterms:available>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/59650/3/Kaltenbach_2-1ofyba49ud2jr5.pdf"/>
<dcterms:issued>2022</dcterms:issued>
<dcterms:title>The Levenberg-Marquardt Method and its Implementation in Python</dcterms:title>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-01-09T09:38:03Z</dc:date>
<dc:language>eng</dc:language>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dcterms:abstract xml:lang="eng">The Levenberg-Marquardt method is a widely used algorithm applied to solve nonlinear least-squares problems. In this thesis, the Levenberg-Marquardt method is implemented in Python as a trust-region approach based on the works of Moré [Mor78] and Nocedal and Wright [NW06]. After a detailed description of the method, the Python code is presented. The Levenberg-Marquardt method is then tested on seven least-squares problems, including small-residual and large-residual problems as well as a poorly scaled one. In particular, the combination of large residuals and poor scaling makes the method slow, as it needs a large number of iterations to converge. Afterwards, the test results are compared to line search methods, such as the Gauss-Newton method. Regarding the test problems, the Levenberg-Marquardt method performed as the most robust algorithm.</dcterms:abstract>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dc:rights>terms-of-use</dc:rights>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/59650"/>
<dc:creator>Kaltenbach, Marius</dc:creator>
<dc:contributor>Kaltenbach, Marius</dc:contributor>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/59650/3/Kaltenbach_2-1ofyba49ud2jr5.pdf"/>
</rdf:Description>
</rdf:RDF> | |
| kops.date.yearDegreeGranted | 2022 | eng |
| kops.description.openAccess | openaccessgreen | |
| kops.flag.knbibliography | true | |
| kops.identifier.nbn | urn:nbn:de:bsz:352-2-1ofyba49ud2jr5 | |
| kops.location.thesis | Konstanz | eng |
| kops.relation.grantingInstitution | Universität Konstanz | eng |
| relation.isAuthorOfPublication | 4ef1b3f3-2bb6-46ec-bd48-b37825b2f501 | |
| relation.isAuthorOfPublication.latestForDiscovery | 4ef1b3f3-2bb6-46ec-bd48-b37825b2f501 |
Dateien
Originalbündel
1 - 1 von 1
Vorschaubild nicht verfügbar
- Name:
- Kaltenbach_2-1ofyba49ud2jr5.pdf
- Größe:
- 979.12 KB
- Format:
- Adobe Portable Document Format
- Beschreibung:
Lizenzbündel
1 - 1 von 1
Vorschaubild nicht verfügbar
- Name:
- license.txt
- Größe:
- 3.96 KB
- Format:
- Item-specific license agreed upon to submission
- Beschreibung:
