A fast symmetric SVD algorithm for square Hankel matrices

Linear Algebra and Its Applications

Volumn 428, Issue 2-3, 2008, Pages 550-563

  Xu, Wei ^a   Qiao, Sanzheng ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Fast SVD; Hankel matrix; Symmetric SVD; Takagi factorization; Toeplitz matrix

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; VECTORS;

FAST SVD; HANKEL MATRIX; SYMMETRIC SVD; TAKAGI FACTORIZATION; TOEPLITZ MATRIX;

MATRIX ALGEBRA;

EID: 36048954191     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.05.027     Document Type: Article

References (20)

1. Akhiezer N.I., and Krein M. Some Questions in the Theory of Moments (1962), AMS
2. Bain A.D. Chemical exchange in NMR. Process Nucl. Magn. Resonance Spectrosc. 43 (2003) 63-103
3. Bunse-Gerstner A., and Gragg W.B. Singular value decomposition of complex symmetric matrices. J. Comput. Appl. Math. 21 (1988) 41-54
4. Comon P. Independent component analysis, a new concept?. Signal Process. 36 (1994) 287-314
5. Dhillon J.S., and Parlett B.N. Orthogonal eigenvectors and relative gaps. SIAM J. Matrix Anal. Appl. 25 3 (2004) 858-899
6. Dhillon J.S., and Parlett B.N. Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices. Linear Algebra Appl. 387 (2004) 1-28
7. M. Frigo, S.G. Johnson, FFTW for version 3.1, 16 January, 2006. .
8. Golub G.H., and Van Loan C.F. Matrix Computations. 3rd ed. (1996), The Johns Hopkins University Press, Baltimore, MD
9. 2) algorithm for the bidiagonal SVD. Linear Algebra Appl. 358 (2003) 45-70
10. Horn R.A., and Johnson C.R. Matrix Analysis (1996), Cambridge University Press, Cambridge
11. Jain A.K. Fundamentals of Digital Image Processing (1989), Prentice-Hall, Inc., Englewood Cliffs, NY
12. Kailath T., and Sayed A.H. Fast Reliable Algorithms for Matrices with Structures (1999), SIAM, Philadelphia
13. R.M. Larsen, Lanczos bidiagonalization with partial reorthogonalization, Technical Report DAIMI PB-357, Department of Computer Science, Aarhus University, September 1998. .
14. Luk F.T., and Qiao S. A fast singular value algorithm for Hankel matrices. In: Olshevsky V. (Ed). Fast Algorithms for Structured Matrices: Theory and Applications, Contemporary Mathematics vol. 323 (2003), American Mathematical Society
15. S. Qiao, Orthogonalization techniques for the Lanczos tridiagonalization of complex symmetric matrices, in: Franklin T. Luk (Ed.), Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, Proc. SPIE, vol. 5559, 2004, pp. 423-434.
16. S. Qiao, G. Liu, W. Xu, Block Lanczos tridiagonalization of complex symmetric matrices, in: Franklin T. Luk (Ed.), Advanced Signal Processing Algorithms, Architectures, and Implementations XV, Proc. SPIE, vol. 5910, 2005, p. 591010.
17. Schwartz H.R. Tridiagonalization of a symmetric band matrix. Numer. Math. 12 (1968) 231-241
18. Willems P.R., Lang B., and Vomel C. Computing the bidiagonal SVD using multiple relatively robust representations. SIAM J. Matrix Anal. Appl. 28 4 (2006) 907-926
19. W. Xu, S. Qiao, A divide-and-conquer method for the Takagi factorization, Technical Report No. CAS 05-01-SQ, McMaster University, Hamilton, Ont., Canada, 2005.
20. W. Xu, S. Qiao, A twisted factorization method for symmetric SVD of a complex symmetric tridiagonal matrix, Technical Report No. CAS 06-01-SQ, McMaster University, Hamilton, Ont., Canada, 2006.