A fast stable solver for nonsymmetric Toeplitz and quasi-Toeplitz systems of linear equations

SIAM Journal on Matrix Analysis and Applications

Volumn 19, Issue 1, 1998, Pages 107-139

  Chandrasekaran, S ^a   Sayed, Ali H ^b  

^a Santa Barbara   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Displacement structure; Error analysis; Generalized Schur algorithm; Generator matrices; Hyperbolic rotations; QR factorization; Schur complements

Indexed keywords

EID: 0032343445     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479895296458     Document Type: Article

References (19)

1. A. W. BOJANCZYK, R. P. BRENT, AND F. DE HOOG, QR factorization of Toeplitz matrices, Numer. Math., 49 (1986), pp. 81-94.
2. A. W. BOJANCZYK, R. P. BRENT, F. R. DE HOOG, AND D. R. SWEET, On the stability of the Bareiss and related Toeplitz factorization algorithms, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 40-57.
3. A. W. BOJANCZYK, R. P. BRENT, P. VAN DOOREN, AND F. R. DE HOOG, A note on downdating the Cholesky factorization, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 210-221.
4. S. CHANDRASEKARAN AND A. H. SAYED, Stabilizing the generalized Schur algorithm, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 950-983.
5. J. CHUN, Fast Array Algorithms for Structured Matrices, Ph.D. thesis, Stanford University, Stanford, CA, 1989.
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 orthogonalization technique with applications to time series analysis and signal processing, Math. Comp., 40 (1983), pp. 323-336.
8. G. CYBENKO, Fast Toeplitz orthogonalization using inner products, SIAM J. Sci. Statist. Comp., 8 (1987), pp. 734-740.
9. I. GOHBERG, T. KAILATH, AND V. OLSHEVSKY, Fast Gaussian elimination with partial pivoting for matrices with displacement structure, Math. Comp., 64 (1995), pp. 1557-1576.
10. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
11. M. GU, Stable, and Efficient Algorithms for Structured Systems of Linear Equations, Tech. report LBL-37690, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, 1995.
12. G. HEINIG, Inversion of generalized Cauchy matrices and other classes of structured matrices, in Linear Algebra for Signal Processing, A. Bojanczyk and G. Cybenko eds., IMA Vol. Math. Appl. 69, Springer, New York, 1995, pp. 63-81.
13. T. KAILATH AND J. CHUN, Generalized displacement structure for block-Toeplitz, Toeplitz-block, and Toeplitz-derived matrices, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 114-128.
14. T. KAILATH, S. Y. KUNG, AND M. MORF, Displacement ranks of a matrix, Bull. Amer. Math. Soc., 1 (1979), pp. 769-773.
15. T. KAILATH AND A. H. SAYED, Displacement structure: Theory and applications, SIAM Rev., 37 (1995), pp. 297-386.
16. A. H. SAYED, Displacement Structure in Signal Processing and Mathematics, Ph.D. thesis, Stanford University, Stanford, CA, 1992.
17. A. H. SAYED AND T. KAILATH, A look-ahead block Schur algorithm for Toeplitz-like matrices, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 388-413.
18. M. STEWART AND P. VAN DOOREN, Stability issues in the factorization of structured matrices, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 104-118.
19. D. R. SWEET, Fast Toeplitz orthogonalization, Numer. Math., 43 (1984), pp. 1-21.