Free Access
Issue |
ESAIM: M2AN
Volume 29, Number 2, 1995
|
|
---|---|---|
Page(s) | 123 - 170 | |
DOI | https://doi.org/10.1051/m2an/1995290201231 | |
Published online | 31 January 2017 |
- 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. [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- F. L. BAUER, 1974, « Computational Graphs and Rounding Error », SIAM J. Numer. Anal, vol. 11,p. 87-96. [MR: 356482] [Zbl: 0337.65028] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- [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] [Google Scholar]
- [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. [Google Scholar]
- 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] [Google Scholar]
- 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. [Google Scholar]
- G. H. GOLUB & C. F. VAN LOAN, 1983, Matrix Computations, John Hopkins University Press. [Zbl: 0559.65011] [MR: 733103] [Google Scholar]
- C. GUEGUEN, 1987, « An Introduction to Displacement Ranks and Related Fast Algorithms», Signal Processing, vol. XLV, Lacoume Durrani Stora Editors, Elsevier, pp. 705-780. [Google Scholar]
- 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] [Google Scholar]
- P. HENRICI, 1982, Essentials of Numerieal Analysis, Wiley. [MR: 655251] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- J. MAKHOUL, 1975, « Linear Prédiction: A Tutorial Review», Proceeding of IEEE, vol.63, n° 4, pp.561-580. [Google Scholar]
- R. E. MOORE, 1966, Interval Analysis, Prentice-Hall, Englewood cliffs, NJ. [MR: 231516] [Zbl: 0176.13301] [Google Scholar]
- P. H. STERBENZ, 1974, Floating Point Computation, Prentice-Hall, Englewood cliffs, NJ. [MR: 349062] [Google Scholar]
- G. W. STEWART, 1973, Introduction to Matrix Computations, Academic Press. [MR: 458818] [Zbl: 0302.65021] [Google Scholar]
- F. STUMMEL, « Perturbation Theory for Evaluation Algorithms of Arithmetic Expressions », Math. Comput., vol. 37, n° 156, pp. 435-473. [MR: 628707] [Zbl: 0515.65039] [Google Scholar]
- 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] [Google Scholar]
- [24]J. H. WlLKINSON, 1963, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, NJ. [MR: 161456] [Zbl: 1041.65502] [Google Scholar]
- J. H. WlLKINSON, 1965, The Algebraic Eigenvalue Problem, Oxford University Press, London [MR: 184422] [Zbl: 0258.65037] [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
- [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] [Google Scholar]
- [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] [Google Scholar]
- 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] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.