CGLS-GCV: A hybrid algorithm for low-rank-deficient problems

Applied Numerical Mathematics

Volumn 47, Issue 2, 2003, Pages 91-108

  Bazán, Fermín S V ^a  

^a FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

Iterative methods; Rank deficient problems; Signal reconstruction

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; SIGNAL RECONSTRUCTION;

RANK-DEFICIENT PROBLEMS;

PROBLEM SOLVING;

EID: 0142009025     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(03)00060-6     Document Type: Conference Paper

References (28)

1. Bazán F.S.V. Conditioning of rectangular Vandermonde matrices with nodes in the unit disk. SIAM J. Matrix Anal. Appl. 21:2000;679-693.
2. Bazán F.S.V., Bavastri C. An optimized pseudo-inverse algorithm (OPIA) for multi-input multi-output modal parameter identification. Mech. Syst. Signal Process. 10:1996;365-380.
3. Bazán F.S.V., Toint Ph.L. Conditioning of infinite Hankel matrices of finite rank. Systems Control Lett. 41:2000;347-359.
4. F.S.V. Bazán, Ph.L. Toint, M.C. Zambaldi, A conjugate-gradient based method for harmonic retrieval problems that does not use explicit signal subspace computation, Technical Report 16, Department of Mathematics, FUNDP, Namur, Belgium, 1997.
5. Björk Å. Numerical Methods for Least Squares Problems. 1996;SIAM, Philadelphia, PA.
6. Björk Å., Grimme E., Van Dooren P. An implicit shift bidiagonalization algorithm for ill-posed problems. BIT. 34:1994;510-534.
7. Cremona C.F., Brandon H.A. Model order testing in discrete time domain identification methods. Mech. Syst. Signal Process. 6:1992;229-236.
8. de Beer R., van Ormondt D. Analysis of NMR data using time domain fitting procedures. Rudin M., Seelig J. NMR Basic Principles and Progress. 26:1997;201-248 Springer, Berlin.
9. Van der Sluis A. The convergence behaviour of conjugate gradients and Ritz values in various circumstances. Beauwens R., de Groen P. Iterative Methods in Linear Algebra. 1992;49-66 Elsevier, New York.
10. Elden L., Sjöstrom E. Fast computation of signal subspace. Signal Process. 210:1994;763-776.
11. Fierro R., Vanhamme L., Van Huffel S. Total least squares algorithms based on rank-revealing complete orthogonal decompositions. Van Huffel S. Recent Advances in Total Least-Squares Techniques and Errors-in-Variables Modelling. 1997;99-116 SIAM, Philadelphia, PA.
12. Fierro R.D., Hansen P.C., Hansen P.S.K. UTV tools: Matlab templates for rank-revealing UTV decompositions. Numer. Algorithms. 20:1999;165-194.
13. Golub G.H., Heath M.T., Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics. 21:1979;215-223.
14. Golub G.H., Van Loan C.F. Matrix Computations. 3rd Edition: 1996;Johns Hopkins University Press, Baltimore, MD.
15. Hanke M., Hansen P.C. Regularization methods for large-scale problems. Surveys Math. Indust. 3:1993;253-315.
16. Hanke M., Nagy J., Plemmons R. Preconditioned iterative regularization for ill-posed problems. Reichel L., Varga R.S. Numerical Linear Algebra. 1993;141-163 De Gruyter, Berlin.
17. Hansen P.C. Regularization tools, a Matlab package for analysis and solution and solution of discrete ill-posed problems. Numer. Algorithms. 6:1994;1-35.
18. Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems - Numerical Aspects of Linear Inversion. 1997;SIAM, Philadelphia, PA.
19. Hestenes M.R. Pseudoinverses and conjugate gradients. Commun. ACM. 18:1975;40-43.
20. Wedin Per-Åke. Perturbation bounds in connection with singular value decomposition. BIT. 12:1972;99-111.
21. O'Leary D.P., Simmons J.A. A bidiagonalization-regularization procedure for large-scale regularization of ill-posed problems. SIAM J. Sci. Stat. Comput. 2:1981;474-489.
22. Stewart G.W. Error and perturbation bounds for subspaces associated with certain eigenvalue problems. SIAM Rev. 32:1973;727-764.
23. Totz J., Van Den Boogart A., Van Huffel S., Graveron-Demilly D., Dologlou I., Heidler R., Michel D. The use of continuous regularization in the automated analysis of MRS time-domain data. J. Magn. Resonance. 124:1997;400-409.
24. Van Der Veen A., Deprettere E.F., Swindlehurst A.L. Subspace-based signal analysis using singular value decomposition. Proc. IEEE. 81:1993;1277-1309.
25. Van Huffel S., Chen H., Decanniere C., Van Hecke P. Algorithm for time-domain NMR data fitting based on total least squares. J. Magn. Resonance A. 110:1994;228-237.
26. Vanhamme L., Fierro R.D., Van Huffel S., de Beer R. Fast removal of residual water in proton spectra. J. Magn. Resonance. 132:1998;197-203.
27. Xu G., Kailath T. Fast estimation of principal eigenspace using Lanczos algorithm. SIAM J. Matrix Anal. Appl. 15:1994;974-994.
28. Zha H., Zhang Z. Matrices with low-rank-plus-shift structure: Partial SVD and latent semantic indexing. SIAM J. Matrix Anal. Appl. 21:1999;522-536.