# Optimal Hankel Structured Rank-1 Approximation

 dc.contributor.advisor Plonka-Hoch, Gerlind Prof. Dr. dc.contributor.author Knirsch, Hanna Elisabeth dc.date.accessioned 2022-03-10T14:39:35Z dc.date.available 2022-03-17T00:50:08Z dc.date.issued 2022-03-10 dc.identifier.uri http://resolver.sub.uni-goettingen.de/purl?ediss-11858/13917 dc.identifier.uri http://dx.doi.org/10.53846/goediss-9108 dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by/4.0/ dc.subject.ddc 510 de dc.title Optimal Hankel Structured Rank-1 Approximation de dc.type doctoralThesis de dc.contributor.referee Plonka-Hoch, Gerlind Prof. Dr. dc.date.examination 2022-02-16 de dc.description.abstracteng Hankel matrices are closely related to linear time-invariant (LTI) models, which are widely used in areas like system theory, signal processing, computer algebra, or machine learning. The complexity of such a model is related to the rank of this matrix: a simple LTI model corresponds to a Hankel matrix of low rank. Thus, Hankel structured low-rank approximation (SLRA) of a matrix is an important task. de The majority of related approaches from the literature only achieves approximate solutions to the SLRA problem with respect to the Frobenius norm. In contrast, for the special case of the rank-1 Hankel approximation (r1H) problem we characterize optimal solutions both for the Frobenius norm and for the spectral norm. More precisely, we show that the r1H problems can be solved by maximizing special rational functions. Since we are able to compute the optimal solutions numerically, they can serve as benchmarks for different methods engaging in the r1H problem. We also give a complete proof that the famous Cadzow algorithm always converges in the r1H setting. dc.contributor.coReferee Lorenz, Dirk Prof. Dr. dc.subject.eng Hankel structure de dc.subject.eng rank-1 Hankel matrices de dc.subject.eng structured low-rank approximation de dc.subject.eng Frobenius norm de dc.subject.eng spectral norm de dc.subject.eng Cadzow algorithm de dc.identifier.urn urn:nbn:de:gbv:7-ediss-13917-0 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematics (PPN61756535X) de dc.description.embargoed 2022-03-17 de dc.identifier.ppn 1795322519
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