Structured low-rank approximation and its applications
Structured low-rank approximation and its applications
Fitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured. We outline applications in system theory (approximate realization, model reduction, output error and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on the variable projections and alternating projections methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm), constraints on the data matrix (e.g., nonnegativity), and data structures (e.g., kernel mapping). Related problems are rank minimization and structured pseudospectra.
Low-rank approximation, total least squares, system identification, errors-in-variables modeling, behaviors.
891-909
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
April 2008
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Markovsky, Ivan
(2008)
Structured low-rank approximation and its applications.
Automatica, 44, .
Abstract
Fitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured. We outline applications in system theory (approximate realization, model reduction, output error and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on the variable projections and alternating projections methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm), constraints on the data matrix (e.g., nonnegativity), and data structures (e.g., kernel mapping). Related problems are rank minimization and structured pseudospectra.
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Published date: April 2008
Keywords:
Low-rank approximation, total least squares, system identification, errors-in-variables modeling, behaviors.
Organisations:
Southampton Wireless Group
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Local EPrints ID: 263379
URI: http://eprints.soton.ac.uk/id/eprint/263379
ISSN: 0005-1098
PURE UUID: d3c58153-0647-49b9-a857-6da1ce3dd94d
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Date deposited: 08 Feb 2007
Last modified: 14 Mar 2024 07:31
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Author:
Ivan Markovsky
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