High-performance numerical algorithms and software for structured total least squares

Journal of Computational and Applied Mathematics

Volumn 180, Issue 2, 2005, Pages 311-331

  Markovsky, Ivan ^a   Van Huffel, Sabine ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Deconvolution; Numerical linear algebra; Parameter estimation; Structured total least squares; System identification

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; CONVOLUTION; IDENTIFICATION (CONTROL SYSTEMS); MATRIX ALGEBRA; OPTIMIZATION; PARAMETER ESTIMATION;

DATA MATRIX; DECONVOLUTION; STRUCTURED TOTAL LEAST SQUARES;

LEAST SQUARES APPROXIMATIONS;

EID: 18644371114     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.11.003     Document Type: Article

References (28)

1. GSL - GNU Scientific Library, http://www.gnu.org/software/gsl/.
2. T. Abatzoglou J. Mendel G. Harada The constrained total least squares technique and its application to harmonic superresolution IEEE Trans. Signal Process. 39 1991 1070-1087
3. M. Aoki P.C. Yue On a priori error estimates of some identification methods IEEE Trans. Automatic Control 15 5 1970 541-548
4. Y. Bresler A. Macovski Exact maximum likelihood parameter estimation of superimposed exponential signals in noise IEEE Trans. Acoust. Speech Signal Process. 34 1986 1081-1089
5. J. Cadzow Signal enhancement-a composite property mapping algorithm IEEE Trans. Signal Process. 36 1988 49-62
6. G. Cirrincione G. Ganesan K. Hari S. Van Huffel Direct and neural techniques for the data least squares problem, in: International Symposium on the Mathematical Theory of Networks and Systems (MTNS) 2000 Perpignan, France
7. 2 approximation problems Linear Algebra Appl. 188-189 1993 163-207
8. B. De Moor Total least squares for affinely structured matrices and the noisy realization problem IEEE Trans. Signal Process. 42 11 1994 3104-3113
9. B. De Moor, Daisy: Database for the identification of systems, Department of Electrical Engineering, ESAT/SISTA, K.U. Leuven, Belgium, URL: Http://www.esat.kuleuven.ac.be/sista/daisy/, 1998.
10. G.H. Golub C.F. Van Loan An analysis of the total least squares problem SIAM J. Numer. Anal. 17 1980 883-893
11. P. Guillaume R. Pintelon A Gauss-Newton-like optimization algorithm for "weighted" nonlinear least-squares problems IEEE Trans. Signal Process. 44 9 1996 2222-2228
12. W. Ku R.H. Storer Ch. Georgakis Disturbance detection and isolation by dynamic principle component analysis Chemometr. Intell. Lab. Systems 30 1995 179-196
13. A. Kukush, I. Markovsky, S. Van Huffel, Consistency of the structured total least squares estimator in a multivariate errors-in-variables model, J. Statist. Plann. Inference, to appear.
14. P. Lemmerling B. De Moor S. Van Huffel On the equivalence of constrained total least squares and structured total least squares IEEE Trans. Signal Process. 44 1996 2908-2911
15. P. Lemmerling N. Mastronardi S. Van Huffel Fast algorithm for solving the Hankel/Toeplitz structured total least squares problem Numer. Algorithms 23 2000 371-392
16. I. Markovsky S. Van Huffel A. Kukush On the computation of the structured total least squares estimator Numer. Linear Algebra Appl. 11 2004 591-608
17. I. Markovsky, S. Van Huffel, R. Pintelon, Block-Toeplitz/Hankel structured total least squares, SIAM J. Matrix Anal. Appl., to appear.
18. I. Markovsky, J.C. Willems, P. Rapisarda, B. De Moor, Algorithms for deterministic balanced subspace identification, Automatica, to appear.
19. I. Markovsky, J.C. Willems, S. Van Huffel, B. De Moor, R. Pintelon, Application of structured total least squares for system identification and model reduction, Technical Report 04-51, Department of Electrical Engineering, K.U. Leuven, 2004.
20. D. Marquardt An algorithm for least squares estimation of nonlinear parameters SIAM J. Appl. Math. 11 1963 431-441
21. N. Mastronardi P. Lemmerling S. Van Huffel Fast structured total least squares algorithm for solving the basic deconvolution problem SIAM J. Matrix Anal. 22 2000 533-553
22. B. Roorda C. Heij Global total least squares modeling of multivariate time series IEEE Trans. Automat. Control 40 1 1995 50-63
23. J.B. Rosen H. Park J. Glick Total least norm formulation and solution of structured problems SIAM J. Matrix Anal. 17 1996 110-128
24. M. Schuermans P. Lemmerling S. Van Huffel Structured weighted low rank approximation Numer. Linear. Algebra Appl. 11 2004 609-618
25. S. Van Huffel H. Park J.B. Rosen Formulation and solution of structured total least norm problems for parameter estimation IEEE Trans. Signal Process. 44 10 1996 2464-2474
26. S. Van Huffel V. Sima A. Varga S. Hammarling F. Delebecque High-performance numerical software for control IEEE Control Systems Mag. 24 2004 60-76
27. S. Van Huffel J. Vandewalle The Total Least Squares Problem: Computational Aspects and Analysis 1991 SIAM Philadelphia
28. P. Van Overschee B. De Moor Subspace Identification for Linear Systems: Theory, Implementation, Applications 1996 Kluwer Academic Publishers Dordrecht