Seminar 24th November 2010 1 p.m. University of Southampton, Building 54, Room 10B (Room 10037 on the 10th Floor)
Low-Rank Approximation and Its Applications
Ivan Markovsky
University of Southampton, ECS
- Web page
- http://www.symbiosis.soton.ac.uk/events.php
- Categories
- Scientific Computing
- Submitter
- Petrina Butler
ABSTRACT
Low-rank approximation is a unifying theme in data modelling. A matrix constructed from the data being rank deficient implies that there is an exact low complexity linear model for the data. Moreover, the rank of the data matrix corresponds to the complexity of the model. In the generic case when an exact low-complexity model does not exist, the aim is to find an model that fits the data approximately. The approach that we present is to find small modification of the data that makes the modified data exact. The exact model for the modified data is an optimal approximate model for the original data. The corresponding computational problem is low-rank approximation. Applications in system theory, signal processing, computer algebra, and curve fitting will be used to illustrate the general concept.
References:
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I. Markovsky, Structured low-rank approximation and its applications, Automatica, 44:891--909, 2007
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I. Markovsky and S. Van Huffel, Overview of total least squares methods, Signal Processing, 87:2283--2302, 2007.
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I. Markovsky, et al., Exact and Approximate Modeling of Linear Systems: A Behavioral Approach, SIAM, 2006.
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