Stabilité numérique de l'algorithme de Levinson

 Access to full text

 Full (PDF)

1. [1] S. T. ALEXANDER & ZONG M. RHEE, 1987, Analytical Finite Precision Results for Burg's Algorithm and the Autocorrelation Method for Linear Prediction, IEEE Trans. on ASSP, 35, n° 5, pp. 626-634. 
2. [2] R. R. BITMEAD & B. D. O. ANDERSON, 1980, Asymptotically Fast Solution of Toeplitz and Related Systems of Linear Equations, Linear Algebra & Its Applications, 34, pp. 103-116. Zbl0458.65018MR591427
3. [3] A. BJÖRCK, 1991, « Errors Analysis of Least Squares Algorithms », NATO ASI Series, vol. F 70, Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, Edited by G. H, Golub and P. Van Dooren, Springer-Verlag Berlin Heidelberg, pp. 41-73. Zbl0757.65047MR1150058
4. [4] F. L. BAUER, 1974, « Computational Graphs and Rounding Error », SIAM J. Numer. Anal, vol. 11,p. 87-96. Zbl0337.65028MR356482
5. [5] J. R. BUNCH, 1985, « Stability of Methods for Solving Toeplitz Systems of Equations », SIAM J. Sci. Stat. Comput., vol. 6, n° 2, pp.349-364. Zbl0569.65019MR779410
6. [6] J. R. BUNCH, 1987, « The Weak and Strong Stability of Algorithms in Numerieal Linear Algebra », Linear Algebra & Its Applications, 88/89, pp.49-66. Zbl0652.65032MR882440
7. [7] J. R. BUNCH, 1991, « The weak Stability of Algorithms of Matrix Computations », NATO ASI Séries, vol. F 70, Numerical Linear Algebra Digital Signal Processing and Parallel Algorithms, Edited by G. H. Golub and P. Van Dooren, Springer-Verlag Berlin Heidelberg, pp. 429-433. Zbl0738.65011MR1150074
8. [8a] J. R. BUNCH, W. DEMMEL & C. F. VAN LOAN, 1989, « The Strong Stability of Algorithms for solving Symmetric Linear Systems », SIAM J. Matr. Anal. Appl., vol. 10, n° 4, pp. 494-499. Zbl0687.65021MR1016798
9. [8b] F. CHATELIN, V. FRAYSSÉ & T. BRACONNIER. 1993, « Qualitative Computing: elements of a theory for finite precision computation », Tech. report CERFACS TR/PA/93/12. Lecture Notes for the Workshop on Reliability of Computations, March 30-April 1, Toulouse. 
10. [9] G. CYBENKO, 1980, « The Numerical Stability of the Levinson-Durbin Algorithm for Toeplitz Systems of Equations», SIAM J. Sci. Stat. Comput., vol. 1, n°3, pp. 303-319. Zbl0474.65026MR596026
11. [10] P. FRANÇOIS, 1989, Contribution à l'Etude de Méthodes de Contrôle Automatique de l'Erreur d'arrondi, la Méthodologie SCALP ; Thèse de Doctorat de l'INPG, Grenoble. 
12. [11] G. H. GOLUB & C. F. VAN LOAN, 1983, Matrix Computations, John Hopkins University Press. Zbl0559.65011MR733103
13. [12] C. GUEGUEN, 1987, « An Introduction to Displacement Ranks and Related Fast Algorithms», Signal Processing, vol. XLV, Lacoume Durrani Stora Editors, Elsevier, pp. 705-780. 
14. [13] F. G. GUSTAVSON & D. Y. YUN, 1989, « Fast Algorithm of Rational Hermite Approximation and Solution of Toeplitz Systems», IEEE Trans. on Circuits and Systems, vol. CAS-26, n° 9, pp. 750-755. Zbl0416.65008MR549385
15. [14] P. HENRICI, 1982, Essentials of Numerieal Analysis, Wiley. MR655251
16. [15] F. de HOOG, « A New Algorithm for Solving Toeplitz Systems of Equations», Linear Algebra & Its Applications, 88/89, pp. 123-138. Zbl0621.65014MR882445
17. [16] K. JAINANDUNSING & E. F DEPRETTERE, « A New Class of Parallel Algorithms for Solving Systems of Linear Equations», SIAM J. Sci. Stat. Comput., vol. 10, n°5, pp.880-912. Zbl0677.65021MR1009545
18. [17] T. KAILATH, A. VIEIRA & M. MORF, 1978, « Inverse of Toeplitz Operators Innovations and Orthogonal Polynomials », SIAM Review, vol.20, n° 1, pp. 106-119. Zbl0382.47013MR512865
19. [18] J. MAKHOUL, 1975, « Linear Prédiction: A Tutorial Review», Proceeding of IEEE, vol.63, n° 4, pp.561-580. 
20. [19] R. E. MOORE, 1966, Interval Analysis, Prentice-Hall, Englewood cliffs, NJ. Zbl0176.13301MR231516
21. [20] P. H. STERBENZ, 1974, Floating Point Computation, Prentice-Hall, Englewood cliffs, NJ. MR349062
22. [21] G. W. STEWART, 1973, Introduction to Matrix Computations, Academic Press. Zbl0302.65021MR458818
23. [22] F. STUMMEL, « Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions », Math. Comput., vol. 37, n° 156, pp. 435-473. Zbl0515.65039MR628707
24. [23] W. F. TRENCH, 1964, « An Algorithm For the Inverson Finite Toeplitz Matrices», SIAM J. Applied Math., vol. 12, pp. 512-522. Zbl0131.36002MR173681
25. [24] J. H. WlLKINSON, 1963, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, NJ. Zbl1041.65502MR161456
26. [25] J. H. WlLKINSON, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, London Zbl0258.65037MR184422
27. [26] S. ZOHAR, 1969, « Toeplitz Matrix Inversion : The Algorithm of W. F. Trench», Journal of the ACM, vol. 16, n° 4, pp. 592-601. Zbl0194.18102MR247762
28. [27] S. ZOHAR, 1974, « The Solution of a Toeplitz set of Linear Equations », Journal of ACM, vol. 21, n° 1, pp. 272-276. Zbl0276.65014MR343567
29. [28] T. F. CHAN & P. C. HANSEN, 1992, « A Look-ahead Levinson Algorithm for Indefinite Toeplitz Systems », SIAM J. Matrix Anal. Appl., vol. 13, n° 2, pp. 490-506. Zbl0752.65020MR1152765
30. [29] D. J. HIGHAM & N. J. HIGHAM, 1992, « Backward Error and Condition of Structured Linear Systems », SIAM J. Matrix Anal. Appl., vol. 13, n° 1, pp. 162-175. Zbl0747.65028MR1146659
31. [30] C. J. ZAROWSKI, 1992, « A Schur Algorithm and Linearly Connected Processor Array for Toeplitz-plus-Hankel Matrices», IEEE Trans. on Signal Processing, vol. 40, n° 8, pp. 2065-2078. Zbl0756.65042