Backward perturbation bounds for linear least squares problems

SIAM Journal on Matrix Analysis and Applications

Volumn 20, Issue 2, 1998, Pages 363-372

  Gu, Ming ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Linear least squares problem; Perturbation; Stability

Indexed keywords

EID: 0032622963     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479895296446     Document Type: Article

References (20)

1. E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, S. OSTROUCHOV, AND D. SORENSEN, LAPACK Users' Guide, 2nd ed., SIAM, Philadelphia, PA, 1994.
2. A. BOJANCZYK AND R. P. BRENT, Parallel solution of certain Toeplitz least-squares problems, Linear Algebra Appl., 77 (1986), pp. 43-60.
3. A. W. BOJANCZYK, R. P. BRENT, AND F. DE HOOG, QR factorization of Toeplitz matrices, Numer. Math., 49 (1986), pp. 81-94.
4. R. P. BRENT, Parallel algorithms for Toeplitz systems, in Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, G. H. Golub and P. Van Dooren, eds., Springer, 1990.
5. P. A. BUSINGER AND G. H. GOLUB, Linear least squares solutions by Householder transformations, Numer. Math., 7 (1965), pp. 269-276.
6. J. CHUN, T. KAILATH, AND H. LEV-ARI, Fast parallel algorithms for QR and triangular factorization, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 899-913.
7. G. CYBENKO, A general orthorgonalization technique with applications to time series analysis and signal processing, Math. Comp., 40 (1983), pp. 323-336.
8. G. CYBENKO, Fast Toeplitz orthorgonalization using inner products, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 734-740.
9. M. GU, New fast algorithms for structured linear least squares problems, SIAM J. Matrix Anal. Appl., 20 (1998), pp. 244-269.
10. M. GU AND S. C. EISENSTAT, A divide-and-conquer algorithm for the bidiagonal SVD, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 79-92.
11. N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, 1996.
12. R. KARLSON AND B. WALDÉN, Practical estimation of optimal backward perturbation bounds for the linear least square problem, BIT, 1996, submitted.
13. R.-C. LI, Solving Secular Equations Stably and Efficiently, manuscript, October 1992.
14. F. T. LUK AND S. QIAO, A fast but unstable orthogonal triangularization technique for Toeplitz matrices, Linear Algebra Appl., 88/89 (1987), pp. 495-506.
15. J. G. NAGY, Fast inverse QR factorization for Toeplitz matrices, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 1174-1183.
16. H. PARK AND L. ELDÉN, Stability Analysis and Fast Algorithms for Triangularization of Toeplitz Matrices, Tech. report Lith-Mat-R-95-16, Department of Mathematics, Linköping University, Sweden, May 1995.
17. S. QIAO, Hybrid algorithm for fast Toeplitz orthogonalization, Numer. Math., 53 (1988), pp. 351-366.
18. G. W. STEWART, Introduction to Matrix Computations, Academic Press, New York, 1973.
19. D. R. SWEET, Fast Toeplitz orthogonalization, Numer. Math., 43 (1984), pp. 1-21.
20. B. WALDÉN, R. KARLSON, AND J.-G. SUN, Optimal backward perturbation bounds for the linear least square problem, Numer. Linear Alg. Appl., 2 (1995), pp. 271-286.