Structured low-rank approximation and its applications

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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 heuristics and local optimization methods are presented. Generalizations of the lowrank approximation problem result from different approximation criteria (e.g., weighted norm) and constraints on the data matrix (e.g., nonnegativity). Related pro...
Ivan Markovsky
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2008
Authors Ivan Markovsky
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