Computing the generalized singular values/vectors of large sparse or structured matrix pairs

Numerische Mathematik

Volumn 72, Issue 3, 1996, Pages 391-417

  Zha, Hongyuan ^a  

^a The Pennsylvania State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030550056     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050175     Document Type: Article

References (33)

1. Bai, Z., Zha, H. (1993): A new preprocessing algorithm for computing the generalized singular value decomposition. SIAM J. Sci. Stat. Comput. 14, 1007-1012
2. n. Elsevier, North Holland, 1991
3. Chan, R., Nagy, J., Plemmons, B. (1992): Circulant preconditioned toeplitz least squares iteration. Technical Report 957, IMA, University or Minnesota
4. Cullum, J., Willoughby, R.A., Lake, M. (1983): A Lanczos algorithm for computing singular values and vectors of large matrices. SIAM J. Sci. Stat. Comput. 4, 197-215
5. Demmel, J., Veselić, K. (1989): Jacobi's method is more accurate than QR. Technical Report 468, Computer Science Department, New York University
6. Golub, G.H., Luk, F.T., Overton, M.L. (1981): A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. ACM Trans. Math. Software 7, 149-169
7. Golub, G.H., Van Loan, C.F. (1989): Matrix computations, 2nd edn. Johns Hopkins University Press, Baltimore, Maryland
8. Golub, G.H., Zha, H.: The canonical correlations and their numerical computation. In: Bojanczky, A., Cybenko, G. (eds.) Linear algebra for signal processing. Berlin, Springer (to appear)
9. Grimes, R.G., Lewis, J.G., Simon, H.D. (1994): A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems. SIAM J. Matrix Anal. Appl. 15, 228-272
10. Kaufman, L. (1993): An algorithm for the banded symmetric generalized matrix eigenvalue problem. SIAM J. Matrix Anal. Appl. 14, 372-389
11. De Moor, B., Zha, H.: (1991): A tree of generalizations of the ordinary singular value decomposition. Lin. Algebra Appl. 147, 469-500
12. Paige, C.C. (1974): Bidiagonalization of matrices and solution of linear systems. SIAM J. Numer. Anal. 11, 197-209
13. Paige, C.C. (1984): A note on a result of Sun Ji-guang: Sensitivity of the cs and gsv decomposition. SIAM J. Numer. Anal. 21, 186-191
14. Paige, C.C. (1986): Computing the generalized singular value decomposition. SIAM J. Sci. Stat. Comput. 7, 1126-1146
15. Paige, C.C., Saunders, M.A. (1981): Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18, 398-405
16. Paige, C.C., Saunders, M.A. (1982): LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software 8, 43-71
17. Parlett, B.N., Scott, D. (1979): The Lanczos algorithm with selective orthogonalization. Math. Comput. 22, 217-238
18. Parlett, B.N. (1980): The symmetric eigenvalue problem. Prentice-Hall, Englewood Cliffs, New Jersey
19. Simon, H.D. (1984): Analysis of the symmetric Lanczos algorithm with reorthogonalization methods. Lin. Algebra Appl. 61, 103-131
20. Simon, H.D. (1984): The Lanczos algorithm with partial reorthogonalization. Math. Comput. 42, 115-142
21. Speiser, J. (1989): Linear algebra problems arising from signal processing. Invited Presentation 3, SIAM Annual Meeting
22. Speiser, J., Van Loan, C. (1984): Signal processing using the generalized signular value decomposition. SPIE, Real Time Signal Proc. VII, 495, 47-55
23. Stewart, G.W. (1977): On the perturbation of pseudo-inverses, projections, and linear least squares problems. SIAM Review 19, 634-662
24. Stewart, G.W. (1982): Computing the CS decomposition of a partitioned orthogonal matrix. Numer. Math. 40, 297-306
25. Stewart, G.W. (1983): A method for computing the generalized singular value decomposition. In: Kågström, B., Ruhe, A. (eds.) Matrix pencils, pp. 207-220. New York, Springer
26. Sun, J.-G. (1983): Perturbation analysis for the generalized singular value decomposition. SIAM J. Numer. Anal. 20, 611-625
27. Van Huffel, S., Vandewalle, J. (1989): Analysis and properties of the generalized total least squares problem AX ≈ B when some or all columns of A are subject to errors. SIAM J. Matrix Anal. Appl. 10, 294-315
28. Van Loan, C.F. (1976): Generalizing the singular value decomposition. SIAM J. Numer. Anal. 13, 76-83
29. Van Loan, C.F. (1985): Computing the CS and the generalized singular value decompositions. Numer. Math. 46, 479-491
30. Van Loan, C.F. (1987): A unitary method for the ESPRIT direction-of-arrival estimation algorithm. SPIE Advanced Alg. Arch. Signal Proc. 826, 170-176
31. Wang, S., Zhao, S. (1991): An algorithm for Ax = λBx with positive definite A and B. SIAM J. Matrix Anal. Appl. 12, 654-660
32. Zha, H. (1993): The singular value decompositions: theory, algorithms and applications. PhD thesis, Stanford University
33. Zha, H.: An inexact alternating projection method for computing the canonical correlations. Manuscript in preparation