A lookahead algorithm for the solution of block Toeplitz systems

Linear Algebra and Its Applications

Volumn 266, Issue 1-3, 1997, Pages 291-335

  Van Barel, Marc ^a   Bultheel, Adhemar ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944441625     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)00013-X     Document Type: Article

References (28)

1. A. W. Bojanczyk and G. Heinig, A multi-step algorithm for Hankel matrices, J. Complexity 10(1):142-164 (Mar. 1994).
2. S. Cabay, A. Jones, and G. Labahn, Computation of numerical Padé-Hermite and simultaneous Padé systems I: Near inversion of generalized Sylvester matrices, SIAM J. Matrix Anal. Appl. 17:248-267(1996).
3. S. Cabay, A. Jones, and G. Labahn, Computation of numerical Padé-Hermite and simultaneous Padé systems II: A weakly stable algorithm, SIAM J. Matrix Anal. Appl. 17:268-297 (1996).
4. S. Cabay, A. R. Jones, and G. Labahn, Algorithm 766: A Stable Algorithm for Multidimensional Padé Systems and the Inversion of Generalized Sylvester Matrices, Technical Report TR 94-07, Dept. of Computing Science, Univ. of Alberta, Edmonton, Alberta, Canada, Mar. 1994.
5. S. Cabay, A. R. Jones, and G. Labahn, Experiments with a weakly stable algorithm for computing Padé-Hermite and simultaneous Padé approximants, ACM Trans. Math. Software 23:91-110 (1997).
6. S. Cabay and R. Meleshko, A weakly stable algorithm for Padé approximants and the inversion of Hankel matrices, SIAM J. Matrix Anal. Appl. 14:735-765 (1993).
7. T. F. Chan and Per C. Hansen, A look-ahead Levinson algorithm for general Toeplitz systems, IEEE Trans. Signal Process. 40(5): 1079-1090 (1992).
8. T. F. Chan and Per C. Hansen, A look-ahead Levinson algorithm for indefinite Toeplitz systems, SIAM J. Matrix Anal. Appl. 13(2):490-506 (1992).
9. R. W. Freund, A look-ahead Bareiss algorithm for general Toeplitz matrices, Numer. Math. 68:35-69 (Aug. 1994).
10. R. W. Freund and H. Zha, Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems, Linear Algebra Appl. 188/189:255-303 (1993).
11. R. W. Fruend and H. Zha, A look-ahead strategy for the solution of general Hankel systems, Numer. Math. 64:295-322 (1993).
12. K. Gallivan, S. Thirumalai, and P. Van Dooren, A look-ahead Schur algorithm, in Fifth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, June 1994, pp. 450-454.
13. K. Gallivan, S. Thirumalai, P. Van Dooren, and V. Vermaut, High performance algorithms for Toeplitz and block Toeplitz matrices, Linear Algebra Appl. 241-243:343-388 (1996).
14. K. Gallivan, S. Thirumalai, and P. Van Dooren, A block Toeplitz look-ahead Schur algorithm, in SVD and Signal Processing 111 (M. Moonen and B. De Moor, Eds.), Elsevier, Amsterdam, 1995, pp. 199-206.
15. I. Gohberg, T. Kailath, and V. Olshevsky, Fast Gaussian elimination with partial pivoting for matrices with displacement structure, Math. Comp. 64(212):1557-1576 (1995).
16. I. Gohberg and T. Shalom, On Bezoutians of nonsquare matrix polynomials and inversion of matrices with nonsquare blocks, Linear Algebra Appl. 137/138:249-323 (1990).
17. G. H. Golub and Ch. F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U.P., Baltimore, 1989.
18. M. Gutknecht and M. Hochbruck, Optimized look-ahead recurrences for adjacent rows in the Padé table, BIT 36:264-286 (1996).
19. M. H. Gutknecht, Stable row recurrences for the Padé table and generically superfast lookahead solvers for non-Hermitian Toeplitz systems, Linear Algebra Appl. 188/189:351-422 (1993).
20. M. H. Gutknecht and M. Hochbruck, Look-ahead Levinson-and Schur-type recurrences in the Padé table, Electron. Trans. Numer. Anal. 2:104-129 (1994).
21. M. H. Gutknecht and M. Hochbruck, Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems, Numer. Math., 70:181-228 (1995).
22. M. H. Gutknecht and M. Hochbruck, The stability of inversion formulas for Toeplitz matrices, Linear Algebra Appl. 223/224:307-324 (1995).
23. G. Heinig, Transformation approaches for fast and stable solution of Toeplitz systems and polynomial equations, in Proceedings of the International Workshop "Recent Advances in Applied Mathematics," Kuwait, May 1996, pp. 223-238.
24. G. Heinig and A. Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. I. Transformations, Linear Algebra Appl. 254(1-3):193-239 (1997).
25. G. Heinig and A. Bojanczyk, Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices. II. Algorithms, Linear Algebra Appl., to appear.
26. T. Huckle, A look-ahead algorithm for solving nonsymmetric linear Toeplitz equation, in Fifth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, June 1994, pp. 455-459.
27. T. Kailath and A. Sayed, Displacement structure: Theory and applications, SIAM Rev. 37(3):297-386 (1995).
28. M. Van Barel and A. Bultheel, A Look-ahead Algorithm for the Solution of Block Toeplitz Systems, Technical Report TW224, Dept. of Computer Science, K.U. Leuven, March (rev. May, Sept.) 1995, 34 pp.