System identification: theory for the user
System identification: theory for the user
From time series to linear system—Part III. Approximate modelling
Automatica (Journal of IFAC)
Algorithms for global total least squares modelling of finite multivariable time series
Automatica (Journal of IFAC)
A Stable and Efficient Algorithm for the Indefinite Linear Least-Squares Problem
SIAM Journal on Matrix Analysis and Applications
Structured Perturbations Part I: Normwise Distances
SIAM Journal on Matrix Analysis and Applications
Block-Toeplitz/Hankel Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
A Global Solution for the Structured Total Least Squares Problem with Block Circulant Matrices
SIAM Journal on Matrix Analysis and Applications
Exact and Approximate Modeling of Linear Systems: A Behavioral Approach (Mathematical Modeling and Computation) (Mathematical Modeling and Computation)
A note on structured pseudospectra
Journal of Computational and Applied Mathematics
Survey paper: Errors-in-variables methods in system identification
Automatica (Journal of IFAC)
High-performance numerical algorithms and software for structured total least squares
Journal of Computational and Applied Mathematics
Total least squares for affinely structured matrices and the noisyrealization problem
IEEE Transactions on Signal Processing
The geometry of weighted low-rank approximations
IEEE Transactions on Signal Processing
The Data Least Squares Problem and Channel Equalization
IEEE Transactions on Signal Processing
Algorithms for deterministic balanced subspace identification
Automatica (Journal of IFAC)
Pseudospectra for exponential polynomial matrices
Proceedings of the 2009 conference on Symbolic numeric computation
Computing a structured Gröbner basis approximately
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Journal of Computational and Applied Mathematics
Software for weighted structured low-rank approximation
Journal of Computational and Applied Mathematics
Low rank approximation of the symmetric positive semidefinite matrix
Journal of Computational and Applied Mathematics
Newton-like iteration for determinantal systems and structured low rank approximation
ACM Communications in Computer Algebra
Hi-index | 22.15 |
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.