Stabilité numérique de l'algorithme de Levinson

Kazamarande, Evariste ; Comon, Pierre

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 29 (1995), p. 123-170 / Harvested from Numdam

Détail

Publié le : 1995-01-01

MR 1332479 | Zbl 0829.65030

Bibliographie

[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] 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. | MR 591427 | Zbl 0458.65018

[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. | MR 1150058 | Zbl 0757.65047

[4] F. L. Bauer, 1974, « Computational Graphs and Rounding Error », SIAM J. Numer. Anal, vol. 11,p. 87-96. | MR 356482 | Zbl 0337.65028

[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. | MR 779410 | Zbl 0569.65019

[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. | MR 882440 | Zbl 0652.65032

[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. | MR 1150074 | Zbl 0738.65011

[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. | MR 1016798 | Zbl 0687.65021

[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.

[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. | MR 596026 | Zbl 0474.65026

[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.

[11] G. H. Golub & C. F. Van Loan, 1983, Matrix Computations, John Hopkins University Press. | MR 733103

[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.

[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. | MR 549385 | Zbl 0416.65008

[14] P. Henrici, 1982, Essentials of Numerieal Analysis, Wiley. | MR 655251

[15] F. De Hoog, « A New Algorithm for Solving Toeplitz Systems of Equations», Linear Algebra & Its Applications, 88/89, pp. 123-138. | MR 882445 | Zbl 0621.65014

[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. | MR 1009545 | Zbl 0677.65021

[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. | MR 512865 | Zbl 0382.47013

[18] J. Makhoul, 1975, « Linear Prédiction: A Tutorial Review», Proceeding of IEEE, vol.63, n° 4, pp.561-580.

[19] R. E. Moore, 1966, Interval Analysis, Prentice-Hall, Englewood cliffs, NJ. | MR 231516 | Zbl 0176.13301

[20] P. H. Sterbenz, 1974, Floating Point Computation, Prentice-Hall, Englewood cliffs, NJ. | MR 349062

[21] G. W. Stewart, 1973, Introduction to Matrix Computations, Academic Press. | MR 458818 | Zbl 0302.65021

[22] F. Stummel, « Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions », Math. Comput., vol. 37, n° 156, pp. 435-473. | MR 628707 | Zbl 0515.65039

[23] W. F. Trench, 1964, « An Algorithm For the Inverson Finite Toeplitz Matrices», SIAM J. Applied Math., vol. 12, pp. 512-522. | MR 173681 | Zbl 0131.36002

[24] J. H. Wllkinson, 1963, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, NJ. | MR 161456 | Zbl 1041.65502

[25] J. H. Wllkinson, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, London | MR 184422 | Zbl 0258.65037

[26] S. Zohar, 1969, « Toeplitz Matrix Inversion : The Algorithm of W. F. Trench», Journal of the ACM, vol. 16, n° 4, pp. 592-601. | MR 247762 | Zbl 0194.18102

[27] S. Zohar, 1974, « The Solution of a Toeplitz set of Linear Equations », Journal of ACM, vol. 21, n° 1, pp. 272-276. | MR 343567 | Zbl 0276.65014

[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. | MR 1152765 | Zbl 0752.65020

[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. | MR 1146659 | Zbl 0747.65028

[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. | Zbl 0756.65042