A Lanczos bidiagonalization algorithm for Hankel matrices

Linear Algebra and Its Applications

Volumn 430, Issue 5-6, 2009, Pages 1531-1543

  Browne, Kevin ^a   Qiao, Sanzheng ^a   Wei, Yimin ^b  

^a MCMASTER UNIVERSITY   (Canada)

^b FUDAN UNIVERSITY   (China)

Author keywords

Fast Hankel SVD; Hankel matrix; Lanczos bidiagonalization

Indexed keywords

FAST ALGORITHMS; FAST HANKEL SVD; HANKEL MATRIX; HANKEL MATRIX-VECTOR; HANKEL STRUCTURE; LANCZOS BIDIAGONALIZATION; LANCZOS METHODS; PERFORMANCE IMPROVEMENTS;

SINGULAR VALUE DECOMPOSITION;

EID: 58549091880     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.01.012     Document Type: Article

References (10)

1. 2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem, Ph.D. Thesis, University of California, Berkeley, 1997.
2. Dhillon J.S., and Parlett B.N. Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices. Linear Algebra Appl. 387 (2004) 1-28
3. Golub G.H., and Van Loan C.F. Matrix Computations. third ed. (1996), The Johns Hopkins University Press, Baltimore, MD
4. Gu M., and Eisenstat S.C. A divide-and-conquer algorithm for the bidiagonal SVD. SIAM J. Matrix Anal. Appl. 16 (1995) 79-92
5. Van Loan C.F. Computational Frameworks for the Fast Fourier Transform (1992), SIAM
6. Luk F.T., and Qiao S. A fast eigenvalue algorithm for Hankel matrices. In: Luk F.T. (Ed). Advance Signal Processing Algorithms, Architectures, and Implementations VIII. Proceedings of SPIE vol. 3461 (1998), The International Society for Optical Engineering 249-256
7. 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
8. 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, Proceedings of SPIE, vol. 5559, 2004, pp. 423-434.
9. Simon H.D. The Lanczos algorithm with partial reorthogonalization. Math. Comp. 42 (1984) 15-142
10. Xu W., and Qiao S. A fast SVD algorithm for square Hankel matrices. Linear Algebra Appl. 482 2+3 (2008) 550-563