Structured low-rank approximation and its applications

✍ Scribed by Ivan Markovsky

• Book ID: 104002888
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 364 KB
• Volume: 44
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2007.09.011

✦ Synopsis

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 low-rank approximation problem result from different approximation criteria (e.g., weighted norm) and constraints on the data matrix (e.g., nonnegativity). Related problems are rank minimization and structured pseudospectra.