Error analysis of qr algorithms for computing Lyapunov exponents

Electronic Transactions on Numerical Analysis

Volumn 12, Issue , 2001, Pages 234-251

  McDonald, Edward J ^a   Higham, Desmond J ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Dynamics; Eigenvalues; Orthogonal iteration; Timestepping

Indexed keywords

EID: 3042683310     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. P. G. ClARLET, Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press, Cambridge, 1989.
2. J. W. DEMMEL, Applied Numerical Linear Algebra, SIAM, Philadelphia, 1997.
3. L. DlECI, R. D. RUSSELL, AND E. S. V. VLECK, Unitary integrators and applications to continuous orthornormal techniques, SIAM J. Numer. Anal., 31 (1994), pp. 261-281.
4. -, On the computation ofLyapunov exponents for continuous dynamical systems, SIAM J. Numer. Anal., 34(1997), pp. 402-423.
5. K. GEIST, U. PARLITZ, AND W. LAUTERBORN, Comparison of different methods for computing Lyapunov exponents, Prog. Theor. Phys., 83 (1990), pp. 875-893.
6. G. H. GOLUB AND C. F. V. LOAN, Matrix Computations, John Hopkins University Press, Baltimore and London, 3rd ed., 1996.
7. D. J. HlGHAM, Time-stepping and preserving orthonormality, BIT, 37 (1997), pp. 24-36.
8. A. ISERLES, H. Z. MUNTHE-KAAS, S. P. N0RSETT, AND A. ZANNA, Lie group methods, Acta Numerica, 9(2000), pp. 215-365.
9. J. D. LAMBERT, Numerical Methods for Ordinary Differential Systems, John Wiley & Sons, Chichester, 1991.
10. G. W. STEWART, Methods of simultaneous iteration for calculating eigenvectors of matrices, in Topics in Numerical Analysis II, John J. H. Miller, Academic Press, New York, 1975, pp. 169-185.
11. -, Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices, Numer. Math., 25 (1976), pp. 123-136.
12. J. STOER AND R. BULIRSCH, Introduction to Numerical Analysis, Springer-Verlag, New York, Inc., 2nd ed., 1992.
13. A. M. STUART AND A. R. HUMPHRIES, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, 1996.
14. THE MATHWORKS, INC., MATLAB User's Guide, Natick, Massachusetts, 1992.
15. D. S. WATKINS, Understanding the QR algorithm, SIAM Review, 24 (1982), pp. 427-4140.
16. -, Isospectral flows, SIAM Review, 26 (1984), pp. 379-391.
17. J. H. WlLKINSON, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, 1965.