Analysis of structured low rank approximation as an optimization problem

Gillard, Jonathan William ORCID: https://orcid.org/0000-0001-9166-298X and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 2011. Analysis of structured low rank approximation as an optimization problem. Informatica 22 (4) , pp. 489-505.

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Abstract

In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	structured low rank approximation; Hankel matrix; optimization
Publisher:	IOS Press
ISSN:	0868-4952
Last Modified:	19 Oct 2022 09:51
URI:	https://orca.cardiff.ac.uk/id/eprint/22396

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