Perturbation analysis for two-sided (or complete) orthogonal decompositions

SIAM Journal on Matrix Analysis and Applications

Volumn 17, Issue 2, 1996, Pages 383-400

  Fierro, Ricardo D ^a  

^a CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

Least squares; Orthogonal decompositions; Perturbation; Rank deficiency; Rank revealing; Singular value decomposition; Subspaces

Indexed keywords

EID: 0030536908     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894264491     Document Type: Article

References (20)

1. G. ADAMS, M. F. GRIFFIN, AND G. W. STEWART, Direction-of-arrival estimation using the rank-revealing URV decomposition, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Washington, DC, 1991.
2. J. BARLOW AND H. ZHA, Stable algorithms for downdating two-sided orthogonal decompositions, in SVD and Signal Processing III. Algorithms, Architectures and Applications, M. Moonen and B. De Moor, eds., Elsevier, New York, 1995.
3. M. W. BERRY AND R. D. FIERRO, Two-sided orthogonal decompositions for information retrieval applications, Numer. Linear Algebra Appl., in press.
4. C. H. BISCHOF, Incremental condition estimation, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 312-322.
5. R. D. FIERRO AND J. R. BUNCH, Bounding the subspaces from rank revealing two-sided orthogonal decompositions, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 743-759.
6. _ Perturbation theory for orthogonal projection methods with applications to least squares and total least squares, Linear Algebra Appl., 234 (1996), pp. 71-96.
7. R. D. FIERRO AND P. C. HANSEN, Accuracy of TSVD solutions computed from rank revealing two-sided orthogonal decompositions, Numer. Math., 70 (1995), pp. 453-471.
8. _ Low rank revealing two-sided orthogonal decompositions, Technical Report PAM 94-09, Department of Mathematics, California State University, San Marcos, CA, October 1994; Numer. Algorithms, submitted.
9. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., The John Hopkins University Press, Baltimore, MD, 1989.
10. P. C. HANSEN, The truncated SVD as a method for regularization, BIT, 27 (1987), pp. 534-553.
11. K. J. R. LIU, D. P. O'LEARY, G. W. STEWART, AND Y.-J. J. Wu, URV ESPIRIT for tracking time-varying signals, IEEE Trans. Signal Process., 42 (1994), pp. 3441-3449.
12. L. MIRSKY, Symmetric Gauge Functions and Unitarily Invariant Norms, Quart. J. Math Oxford Ser. (2), 11 (1960), pp. 50-59.
13. H. PARK AND L. ELDÉN, Downdating the rank revealing URV decomposition, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 138-155.
14. D. J. PIERCE, A Sparse URL Rather than an URV Factorization, Mathematics and Engineering Analysis Technical Report MEA-TR-203, Boeing Computer Services, Seattle, WA, 1992.
15. G. W. STEWART, An updating algorithm for subspace tracking, IEEE Trans. Signal Process., 40 (1992), pp. 1535-1541.
16. R. MATHIAS AND G. W. STEWART, A block QR algorithm and the singular value decomposition, Linear Algebra Appl., 182 (1992), pp. 91-100.
17. G. W. STEWART, Updating a rank revealing ULV decomposition, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 494-499.
18. S. VAN HUFFEL AND H. ZHA, An efficient total least squares algorithm based on a rank revealing two-sided orthogonal decomposition, Numer. Algorithms, 4 (1993), pp. 101-133.
19. P.-A. WEDIN, Perturbation bounds in connection with the singular value decomposition, BIT, 12 (1973), pp. 99-111.
20. _ Perturbation theory for pseudoinverses, BIT, 13 (1973), pp. 217-232.