The condition number of Vandermonde matrices and its application to the stability analysis of a subspace method

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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://repositorium.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

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