Optimal Hankel Structured Rank-1 Approximation

Knirsch, Hanna Elisabeth

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. 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.	de
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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