Bounds for the least squares distance using scaled total least squares

Numerische Mathematik

Volumn 91, Issue 1, 2002, Pages 93-115

  Paige, Christopher C ^a   Strakoš, Zdeněk ^b  

^a MCGILL UNIVERSITY   (Canada)

^b INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036013505     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100317     Document Type: Article

References (16)

1. Å. Björck: Numerical Methods for Least Squares Problems. Philadelphia PA: SIAM Publications 1996
2. Å. Björck, P. Heggerness, P. Matstoms: Methods for large scale total least squares problems. SIAM J. Matrix Anal. Appl., 22, 413-429 (2000)
3. G. H. Golub, C. Reinsch: Singular value decomposition and least squares solutions. Numerische Mathematik 14, 403-420 (1970). Also in "Handbook for Automatic Computation Vol. 2: Linear Algebra", by J. H. Wilkinson, C. Reinsch, (eds.), pp. 134-151. New York: Springer 1971
4. G. H. Golub, C. Reinsch: Singular value decomposition and least squares solutions. Numerische Mathematik 14, 403-420 (1970). Also in "Handbook for Automatic Computation Vol. 2: Linear Algebra", by J. H. Wilkinson, C. Reinsch, (eds.), pp. 134-151. New York: Springer 1971
5. G. H. Golub, C. F. Van Loan: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883-893 (1980)
6. G. H. Golub, C. F. Van Loan: Matrix Computations. Baltimore MD: The Johns Hopkins University Press, third ed. 1996
7. A. Greenbaum, M. Rozložník, Z. Strakoš: Numerical behavior of the modified Gram-Schmidt GMRES implementation. BIT 37:3, 706-719 (1997)
8. N. J. Higham: Accuracy and Stability of Numerical Algorithms. Philadelphia PA: SIAM Publications 1996
9. R. A. Horn, C. R. Johnson: Matrix Analysis. Cambridge: Cambridge University Press 1985
10. S. Van Huffel, J. Vandewalle: The Total Least Squares Problem: Computational Aspects and Analysis. Philadelphia PA: SIAM Publications 1991
11. E. M. Kasenally, V. Simoncini: Analysis of a minimum perturbation algorithm for nonsymmetric linear systems. SIAM J. Numer. Anal. 34, 48-66 (1997)
12. J. Liesen, M. Rozložník, Z. Strakoš": On Convergence and Implementation of Residual Minimizing Krylov Subspace Methods. Submitted to SIAM J. Sci. Comput., September 2000
13. C. C. Paige, Z. Strakoš: Scaled total least squares fundamentals. Accepted for publication in Numerische Mathematik, February 2001
14. C. C. Paige, Z. Strakoš: Residual behaviour in minimum residual Krylov subspace methods. Submitted to SIAM J. Sci. Comput., October 2000
15. B. D. Rao: Unified treatment of LS, TLS and truncated SVD methods using a weighted TLS framework. In: Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modelling, pp. 11-20, S. Van Huffel (ed.), Philadelphia PA: SIAM 1997
16. Y. Saad, M. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7, 856-869 (1986)