Structured total least norm for nonlinear problems

SIAM Journal on Matrix Analysis and Applications

Volumn 20, Issue 1, 1998, Pages 14-30

  Rosen, J B ^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; Frequency estimation; Least squares; Linear prediction; Outliers; Overdetermined linear systems; Parameter estimation; Total least norm; Total least squares; Vandermonde matrix

Indexed keywords

EID: 0032217341     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479896301662     Document Type: Article

References (31)

1. T. J. ABATZOGLOU, J. M. MENDEL, AND 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., 234 (1996), pp. 137-161.
3. H. BARKHUIJSEN, R. DE BEER, AND D. VAN ORMONDT, Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals, J. Magnetic Resonance, 73 (1987), pp. 553-557.
4. ∞ linear approximations on a discrete set, Numer. Math., 8 (1966), pp. 295-306.
5. 1 approximation and the analysis of data, Appl. Statistics, 17 (1968), pp. 51-57.
6. D. BATES AND M. LINDSTROM, Nonlinear least squares with conditionally linear parameters, in Proceedings of the Statistical Computing Section, American Statistical Association, Washington, DC, 1986, pp. 152-157.
7. H. CHEN, S. VAN HUFFEL, AND J. VANDEWALLE, Exponential Data Fitting Using the Structured Total Least Norm Technique, Technical report TR 95-18, Departement Elektrotechniek ESAT-SISTA, University of Leuven, Belgium, March, 1995.
8. R. DE BEER AND D. VAN ORMONDT, Analysis of NMR data using time-domain fitting procedures, in In-vivo Magnetic Resonance Spectroscopy I: Probeheads, Radiofrequency Pulses, Spectrum Analysis, NMR Basic Principles and Progress 26, M. Rudin, ed., Springer-Verlag, Berlin, Heidelberg, 1992, pp. 201-248.
9. R. FLETCHER, Practical Methods of Optimization, John Wiley, New York, 1987.
10. G. H. GOLUB AND V. PEREYRA, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Numer. Anal., 10 (1973), pp. 413-432.
11. T. A. GRANDINE, Generating Surface Lofts to Scattered Data, Engineering Computing and Analysis Technical report ECA-TR-157, Boeing Computer Services, Seattle, WA, 1991.
12. L. KAUFMAN, A variable projection method for solving separable nonlinear least squares problems, BIT, 15 (1975), pp. 49-57.
13. L. KAUFMAN AND G. SYLVESTER, Separable nonlinear least squares with multiple right-hand sides, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 68-89.
14. R. KUMARESAN AND D. W. TUFTS, Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise, IEEE Trans. Acoust. Speech Signal Proc., 30 (1982), pp. 833-840.
15. S. Y. KUNG, K. S. ARUN, AND D. V. BHASKAR RAO, State-space and singular value decomposition-based approximation methods for the harmonic retrieval problem, J. Opt. Soc. Amer., 73 (1983), pp. 1799-1811.
16. C. L. LAWSON AND R. J. HANSON, Solving Least Squares Problems, Prentice-Hall, Englewood Cliffs, NJ, 1974.
17. p-norm Problems and Applications, Cornell Theory Center report CTC93TR122, Cornell University, Ithaca, NY, 1993.
18. M. R. OSBORNE, Some special nonlinear least squares problems, SIAM J. Numer. Anal., 12 (1975), pp. 571-592.
19. M. R. OSBORNE AND G. K. SMYTH, A modified Prony algorithm for exponential function fitting, SIAM J. Sci. Comput., 16 (1995), pp. 119-138.
20. H. PARK, J. B. ROSEN, AND J. CLICK, Structure preserving total least norm method and application to parameter estimation, in Proceedings of the 1995 International Conference on Acoustics, Speech and Signal Processing, Vol. 2, 1995, pp. 1141-1144.
21. H. PARK, J. B. ROSEN, AND S. VAN HUFFEL, Structure preserving total least squares method and its application to parameter estimation, SVD and Signal Processing, III: Algorithms, Architectures and Applications, M. Moonen and B. De Moor, eds., Elsevier, New York, 1995, pp. 399-406.
22. M. A. RAHMAN AND K. B. Yu, Total least squares approach for frequency estimation using linear prediction, IEEE Trans. Acous. Speech Signal Proc., 35 (1987), pp. 1440-1454.
23. J. R. RICE AND J. S. WHITE, Norms for smoothing and estimation, SIAM Rev., 6 (1964), pp. 243-256.
24. J. B. ROSEN, H. PARK, AND J. GLICK, Total least norm formulation and solution for structured problems, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 110-128.
25. J. B. ROSEN, H. PARK, AND J. GLICK, Total least norm for linear and nonlinear structured problems, in Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S. Van Huffel, ed., SIAM, Philadelphia, 1996, pp. 203-214.
26. 1 Norm Minimization, Tech. report 98-7, Department UCSD, La Jolla, CA, January 13, 1988 (submitted for publication).
27. 1 approximation, Numer. Math., 51 (1996), pp. 531-543.
28. S. VAN HUFFEL, H. PARK, AND J. B. ROSEN, Formulation and solution of structured total least norm problems for parameter estimation, IEEE Trans. Signal Process., (1996), pp. 2464-2474.
29. S. VAN HUFFEL, L. AERTS, J. BERVOETS, J. VANDEWALLE, C. DECANNIERE, AND P. VAN HECKE, Improved quantitative time-domain analysis of NMR data by total least squares, in Signal Processing VI: Theories and applications, J. Vandewalle, R. Boite, M. Moonen and A. Oosterlinck, eds., Elsevier-North Holland, 1992, pp. III:1721-1724.
30. S. VAN HUFFEL AND J. VANDEWALLE, The Total Least Squares Problem, Computational Aspects and Analysis, SIAM, Philadelphia, 1991.
31. 1 norm, BIT, 31 (1991), pp. 697-710.