Publikation:

The Levenberg-Marquardt Method and its Implementation in Python

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2022

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http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1ofyba49ud2jr5
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Mathematik und Statistik: Publikationen
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Masterarbeit/Diplomarbeit
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Zusammenfassung

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.

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510 Mathematik

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ISO 690KALTENBACH, Marius, 2022. The Levenberg-Marquardt Method and its Implementation in Python [Master thesis]. Konstanz: Universität Konstanz
BibTex
@mastersthesis{Kaltenbach2022Leven-59650,
  year={2022},
  title={The Levenberg-Marquardt Method and its Implementation in Python},
  address={Konstanz},
  school={Universität Konstanz},
  author={Kaltenbach, Marius}
}
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Konstanz, Universität Konstanz, Masterarbeit/Diplomarbeit, 2022
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