The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202103194121
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202103194121
Title: | The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method |
Other Titles: | Die Konditionzahl von Vandermondematrizen und ihre Anwendung für die Stabilitätsanalyse einer Unterraummethode |
Authors: | Nagel, Dominik |
ORCID of the author: | https://orcid.org/0000-0002-4777-7496 |
Thesis advisor: | Prof. Dr. Stefan Kunis |
Thesis referee: | Prof. Dr. Dmitry Batenkov |
Abstract: | This thesis consists of two main parts. First of all, the condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is studied. The first time quantitative bounds for the extreme singular values are proven in the multivariate setting and when nodes of the Vandermonde matrix form clusters. In the second part, an optimized presentation of the deterministic stability analysis of the subspace method ESPRIT is given and results from the first part are applied. |
URL: | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-202103194121 |
Subject Keywords: | Vandermonde matrix; stability analysis; subspace method; ESPRIT; clustered nodes |
Issue Date: | 19-Mar-2021 |
License name: | Attribution 3.0 Germany |
License url: | http://creativecommons.org/licenses/by/3.0/de/ |
Type of publication: | Dissertation oder Habilitation [doctoralThesis] |
Appears in Collections: | FB06 - E-Dissertationen |
Files in This Item:
File | Description | Size | Format | |
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thesis_nagel.pdf | Präsentationsformat | 2,18 MB | Adobe PDF | thesis_nagel.pdf View/Open |
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