Fast robust regression algorithms for problems with Toeplitz structure

Computational Statistics and Data Analysis

Volumn 52, Issue 2, 2007, Pages 1119-1131

  Mastronardi, Nicola ^a   O'Leary, Dianne P ^b  

^a CNR   (Italy)

^b Institute of Advanced Computer Science   (United States)

Author keywords

FIR system identification; Iteratively reweighted least squares; Outliers; Robust regression; Small displacement rank; Toeplitz matrices

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; PROBLEM SOLVING; REGRESSION ANALYSIS;

FIR SYSTEM IDENTIFICATION; OUTLIERS; ROBUST REGRESSION; SMALL DISPLACEMENT RANKS; TOEPLITZ MATRICES;

LINEAR EQUATIONS;

EID: 35148854618     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.05.008     Document Type: Article

References (30)

1. Benzi M., and Ng M.K. Preconditioned iterative methods for weighted Toeplitz least squares problems. SIAM J. Matrix Anal. Appl. 27 (2006) 1106-1124
2. Björck A. Numerical Methods for Least Squares Problems (1996), SIAM, Philadelphia, PA
3. Björck A., and Paige C.C. Solution of augmented linear systems using orthogonal factorizations. BIT 34 (1994) 1-24
4. Bojanczyk A.W., and Steinhardt A.O. Stabilized hyperbolic Householder transformations. IEEE Trans. Acoust. Speech Signal Process. 37 (1989) 1286-1288
5. Chandrasekaran S., and Sayed A.H. Stabilizing the generalized Schur algorithm. SIAM J. Matrix Anal. Appl. 17 (1996) 950-983
6. Coleman D., Holland P., Kaden N., and Klema V. A system of subroutines for iteratively reweighted least squares computations. ACM Trans. Math. Software 6 (1980) 327-336
7. Dyn N., and Ferguson W.E. The numerical solution of equality-constrained quadratic programming problems. Math. Comp. 41 (1983) 165-170
8. Fair R.C. On the robust estimation of econometric models. Ann. Econom. Social Measurement 3 (1974) 667-678 (ref. by Holland, P.W., Welsch, R.E., 1977. Robust regression using iteratively reweighted least-squares. Comm. Statist. Theory, Methods A 6, 813-827)
9. Fang, H.R., O'Leary, D.P., 2006. Modified Cholesky algorithms: a catalog with new approaches, Submitted for publication.
10. Golub G.H., and Van Loan C.F. Matrix Computations. third ed (1996), Johns Hopkins University Press, Baltimore, MD
11. Hansen P.C. Rank-Deficient and Discrete Ill-Posed Problems. Numerical Aspects of Linear Inversion (1998), SIAM Monographs on Mathematical Modeling and Computation. Society for Industrial and Applied Mathematics, Philadelphia, PA
12. Haykin S. Adaptive Filter Theory. fourth ed (2001), Prentice-Hall, Englewood Cliffs, NJ
13. Hinich M.J., and Talwar P.P. A simple method for robust regression. J. Amer. Statist. Assoc. 70 (1975) 113-119
14. Holland P.W., and Welsch R.E. Robust regression using iteratively reweighted least-squares. Comm. Statist. Theory Methods A 6 (1977) 813-827
15. Huber P.H. Robust estimation of a location parameter. Ann. Math. Statist. 35 (1964) 73-101
16. Kailath T., and Sayed A.H. Displacement structure: theory and applications. SIAM Rev. 37 (1995) 297-386
17. Kailath T., and Sayed A.H. Fast Reliable Algorithms for Matrices with Structure (1999), SIAM, Philadelphia, PA
18. Kalsi A., and O'Leary D.P. Algorithms for structured total least squares problems with applications to blind image deblurring. J. Res. Nat. Inst. Standards Technol. 111 2 (2006) 113-119
19. Mastronardi N., Lemmerling P., and Van Huffel S. Fast structured total least squares algorithm for solving the basic deconvolution problem. SIAM J. Matrix Anal. Appl. 22 (2001) 533-553
20. Mastronardi N., Van Dooren P., and Van Huffel S. On the stability of the generalized Schur algorithm. Lecture Notes in Comput. Sci. 1988 (2001) 560-567
21. Mastronardi N., Lemmerling P., Kalsi A., O'Leary D.P., and Van Huffel S. Implementation of the regularized structured total least squares algorithms for blind image deblurring. Linear Algebra Appl. 391 (2004) 203-221
22. Nash S.G., and Sofer A. Linear and Nonlinear Programming (1996), McGraw-Hill, New York
23. Ng, M.K., 1996. Fast direct methods for Toeplitz least squares problems. IEEE TENCON '96. Proceedings on Digital Signal Processing Applications, vol. 2, pp. 743-748
24. O'Leary D.P. Robust regression computation using iteratively reweighted least squares. SIAM J. Matrix Anal. Appl. 11 (1990) 466-480
25. O'Leary D.P., and Simmons J.A. A bidiagonalization-regularization procedure for large scale discretizations of Ill-posed problems. SIAM J. Sci. Statist. Comput. (1981) 2474-2489
26. Pruessner A., and O'Leary D.P. Blind deconvolution using a regularized structured total least norm approach. SIAM J. Matrix Anal. Appl. 24 (2003) 1018-1037
27. Rader C.M., and Steinhardt A.O. Hyperbolic Householder transforms. SIAM J. Matrix Anal. Appl. 9 (1988) 269-290
28. Stewart M., and Van Dooren P. Stability issues in the factorization of structured matrices. SIAM J. Matrix Anal. Appl. 18 (1997) 104-118
29. Van Loan, C., 1992. Computational frameworks for the fast Fourier transform. SIAM Frontiers in Applied Mathematics Series, Philadelphia, PA.
30. Watson G.A. Choice of norms for data fitting and function approximation. Acta Numerica 7 (1998) 337-377