Left vs right representations for solving weighted low-rank approximation problems

Linear Algebra and Its Applications

Volumn 422, Issue 2-3, 2007, Pages 540-552

  Markovsky, Ivan ^a   Van Huffel, Sabine ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Parameter optimization; Total least squares; Weighted low rank approximation

Indexed keywords

CONSTRAINT THEORY; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; NUMERICAL METHODS; OPTIMIZATION; PARAMETER ESTIMATION;

PARAMETER OPTIMIZATION; TOTAL LEAST SQUARES; WEIGHTED LOW-RANK APPROXIMATION;

PROBLEM SOLVING;

EID: 33847313774     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.11.012     Document Type: Article

References (13)

1. 2 approximation problems. Linear Algebra Appl. 188-189 (1993) 163-207
2. Eckart G., and Young G. The approximation of one matrix by another of lower rank. Psychometrika 1 (1936) 211-218
3. Gabriel K., and Zamir S. Lower rank approximation of matrices by least squares with any choice of weights. Technometrics 21 (1979) 489-498
4. Manton J., Mahony R., and Hua Y. The geometry of weighted low-rank approximations. IEEE Trans. Signal Process. 51 2 (2003) 500-514
5. Markovsky I., Rastello M.-L., Premoli A., Kukush A., and Van Huffel S. The element-wise weighted total least squares problem. Comput. Statist. Data Anal. 50 1 (2005) 181-209
6. Markovsky I., Willems J.C., Van Huffel S., and De Moor B. Exact and Approximate Modeling of Linear Systems: A Behavioral Approach. Monographs on Mathematical Modeling and Computation vol. 11 (2006), SIAM
7. Premoli A., and Rastello M.-L. The parametric quadratic form method for solving TLS problems with elementwise weighting. In: Van Huffel S., and Lemmerling P. (Eds). Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications (2002), Kluwer 67-76
8. Paige C., and Strakos Z. Core problems in linear algebraic systems. SIAM J. Matrix Anal. Appl. 27 (2005) 861-875
9. Schuermans M., Markovsky I., Wentzell P., and Van Huffel S. On the equivalence between total least squares and maximum likelihood PCA. Anal. Chim. Acta 544 (2005) 254-267
10. Van Loan C., and Pitsianis N. Approximation with Kronecker products. In: Moonen M., and Golub G. (Eds). Linear Algebra for Large Scale and Real Time Applications (1993), Kluwer Publications 293-314
11. Van Huffel S., and Vandewalle J. Analysis and solution of the nongeneric total least squares problem. SIAM J. Matrix Anal. Appl. 9 (1988) 360-372
12. Van Huffel S., and Vandewalle J. The Total Least Squares Problem: Computational Aspects and Analysis (1991), SIAM, Philadelphia
13. Wentzell P., Andrews D., Hamilton D., Faber K., and Kowalski B. Maximum likelihood principle component analysis. J. Chemometrics 11 (1997) 339-366