Survey paper: Structured low-rank approximation and its applications

  • Authors:
  • Ivan Markovsky

  • Affiliations:
  • School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

Quantified Score

Hi-index 22.15

Visualization

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 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.