An algorithm based on orthogonal polynomial vectors for Toeplitz least squares problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1988, Issue , 2001, Pages 27-34

  Van Barel, Marc ^a   Heinig, Georg ^b   Kravanja, Peter ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b KUWAIT UNIVERSITY   (Kuwait)

Author keywords

[No Author keywords available]

Indexed keywords

MATRIX ALGEBRA; NUMBER THEORY; POLYNOMIAL APPROXIMATION;

ALGORITHM FOR SOLVING; BACKWARD STABILITIES; CIRCULANT MATRIX; CONDITION NUMBERS; LEAST SQUARES PROBLEMS; LINEAR LEAST SQUARES PROBLEMS; ORTHOGONAL POLYNOMIAL; TOEPLITZ MATRICES;

LEAST SQUARES APPROXIMATIONS;

EID: 23044525495     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45262-1_4     Document Type: Conference Paper

References (16)

1. A. Bojanczyk, R. Brent, and F. de Hoog, QR factorization of Toeplitz matrices, Numer. Math., 49 (1986), pp. 81–94.
2. A. Bultheel and M. Van Barel, Vector orthogonal polynomials and least squares approximation, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 863–885.
3. 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.
4. G. Cybenko, A general orthogonalization technique with applications to time series analysis and signal processing, Math. Comp., 40 (1983), pp. 323–336.
5. G. Cybenko Fast Toeplitz orthogonalization using inner products, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 734–740.
6. 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.
7. M. Gu, Stable and efficient algorithms for structured systems of linear equations, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 279–306.
8. N. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 1996.
9. S. Qiao, Hybrid algorithm for fast Toeplitz orthogonalization, Numer. Math., 53 (1988), pp. 351–366.
10. D. Sweet, Numerical Methods for Toeplitz matrices, PhD thesis, University of Adelaide, Adelaide, Australia, 1982.
11. D. Sweet Fast Toeplitz orthogonalization, Numer. Math., 43 (1984), pp. 1–21.
12. M. Van Barel and A. Bultheel, A parallel algorithm for discrete least squares rational approximation, Numer. Math., 63 (1992), pp. 99–121.
13. M. Van Barel and A. Bultheel Discrete linearized least squares approximation on the unit circle, J. Comput. Appl. Math., 50 (1994), pp. 545–563.
14. M. Van Barel and A. Bultheel Orthonormal polynomial vectors and least squares approximation for a discrete inner product, Electron. Trans. Numer. Anal., 3 (1995), pp. 1–23.
15. J. Varah, The Prolate matrix, Linear Algebra Appl., 187 (1993), pp. 269–278.
16. B. Waldén, R. Karlson, and J.-g. Sun, Optimal backward perturbation bounds for the linear least squares problem, Numerical Linear Algebra with Applications, 2 (1995), pp. 271–286.