Total least norm formulation and solution for structured problems

SIAM Journal on Matrix Analysis and Applications

Volumn 17, Issue 1, 1996, Pages 110-126

  Rosen, J Ben ^a,b   Park, Haesun ^a   Glick, John ^c  

^a University of Minnesota   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF SAN DIEGO   (United States)

Author keywords

1 norm; 2 norm; Data fitting; Hankel structure; Least squares; Linear prediction; Minimization; Overdetermined linear systems; Structured total least norm; Toeplitz structure; Total least squares; norm

Indexed keywords

EID: 0030550537     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479893258802     Document Type: Article

References (17)

1. T.J. ABATZOGLOU, J.M. MENDEL, G.A. HARADA, The constrained total least squares technique and its application to harmonic superresolution, IEEE Trans. Signal Processing, 39 (1991), pp. 1070-1087.
2. A.A. ANDA AND H. PARK, Self-scaling fast rotations for stiff least squares problems, Linear Algebra Appl., to appear.
3. J. W. DEMMEL, The smallest perturbation of a submatrix which lowers the rank and constrained total least squares problems, SIAM J. Numer. Anal., 24 (1987), pp. 199-206.
4. 2 approximation problems, Linear Algebra Appl., special issue on Numerical Linear Algebra Methods in Control, Signals and Systems, Van Dooren et al., eds., 188-189 (1993), pp. 163-207.
5. R. FLETCHER Practical Methods of Optimization, Vol. 1, Unconstrained Optimization. John Wiley, New York, 1980.
6. E. FOGEL, Total least squares for Toeplitz structures, in Proc. 21st IEEE Conference on Decision and Control, Orlando, 3 (1982), pp. 1003-1004.
7. G. H. GOLUB AND C. F. VAN LOAN, An analysis of the total least squares problem, SIAM J. Numer. Anal., 17 (1980), pp. 883-893.
8. _, Matrix Computations, second edition, Johns Hopkins University Press, Baltimore, 1989.
9. S. HAYKIN, Adaptive Filter Theory, second edition, Prentice Hall, Englewood Cliffs, NJ, 1991.
10. 1 problem, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 410-424.
11. M. A. RAHMAN AND K. B. YU, Total least squares approach for frequency estimation using linear prediction, IEEE Trans. on Acoustic Speech Signal Processing, ASSP-35 (1987), pp. 1440-1454.
12. J.B. ROSEN, H. PARK, AND J. GLICK, Total least norm formulation and solution for structured problems, AHPCRC preprint 94-041, University of Minnesota, July, 1994.
13. S. VAN HUFFEL AND J. VANDEWALLE, Analysis and properties of the generalized total least squares problem AX ≈ B when some or all columns of A are subject to errors, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 294-315.
14. _, The Total Least Squares Problem, Computational Aspects and Analysis, Society for Industrial and Applied Mathematics, Philadelphia, 1991.
15. S. VAN HUFFEL, B. DE MOOR, AND H. CHEN, Relationships between constrained and structured TLS, with applications to signal enhancement, Proc. Internat. Symp. Mathematical Theory for Networks and Systems, Regensburg, Germany, August 2-6, 1993, to appear.
16. C.F. VAN LOAN, On the method of weighting for equality constrained least squares problems, SIAM J. Numer. Anal., 22 (1985), pp. 851-864.
17. G.A. WATSON, On a class of algorithms for total approximation, J. Approx. Theory, 45 (1985), pp. 219-231.