Singular Value Decomposition (SVD), Lyapunov vectors, and Bred vectors: A Bibliography

• B. Legras and R. Vautard, "A guide to Liapunov vectors," in ECMWF seminar proceedings: Predictability, Vol I pp. 141-156, 4-8 September 1995 (pdf)
• A. Trevisan and F. Pancotti, "Periodic orbits, Lyapunov vectors, and singular vectors in the Lorenz system," Journal of Atmospheric Sciences 55 pp. 390-398 (1998) (pdf)

• I. Gilmour, L. Smith, and R. Buizza, "Linear Regime Duration: Is 24 Hours a Long Time in Synoptic Weather Forecasting?" Journal of the Atmospheric Sciences 58 (22) pp. 3525-3539 (2001) (pdf)
• E. Kalnay, M. Corazza, and M. Cai, "Are bred vectors the same as lyapunov vectors?" (http)
• Z. Toth and E. Kalnay, "Ensemble Forecasting at NCEP and the Breeding Method," Monthly Weather Review 125 (12) pp. 3297-3319 (1997) (pdf)
• M. Corazza et al., "Use of the breeding technique in the estimation of the background covariance matrix for a quasi-geostrophic model" (http)
• J. Hansen, L. Smith, "The Role of Operational Constraints in Selecting Supplementary Observations," Journal of the Atmospheric Sciences 57 (17) pp. 2859-2871 (2000) (pdf)
• L. Smith, C. Ziehmann, and K. Fraedrich, "Uncertainty dynamics and predictability in chaotic systems," Quarterly Journal of the Royal Meteorological Society 125 (560) pp. 2855-2886 (1999) (pdf) (ps)
• Z. Toth and E. Kalnay, "Ensemble Forecasting at NMC: The Generation of Perturbations," Bulletin of the American Meteorological Society 74 (12) pp. 2317-2330 (1993) (pdf)
• L. Smith, "Accountability and error in ensemble prediction of baroclinic flows," in ECMWF seminar proceedings: Predictability, Vol I, pp. 351-368, 4-8 September 1995 (pdf)
• An extended introduction to attractors etc.:
  J. Eckmann and D. Ruelle, "Ergodic theory of chaos and strange attractors," Reviews of Modern Physics 57, 617-656 (1985) (pdf)
• R. Samelson, "Lyapunov, Floquet, and singular vectors for baroclinic waves," Nonlinear Processes in Geophysics, 8, 439-448 (2001) (pdf)
• I. Szunyogh, E. Kalnay, and Z. Toth, "A comparison of Lyapunov and optimal vectors in a low-resolution GCM," Tellus 49 A, 200-227 (1997) (pdf)
• Two papers that discuss calculations of Lyapunov vectors and exponents:
  • G. Benettin et al., "Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; A method for computing all of them; Parts 1 and 2," Meccanica, ??, 9-30 (1980) (pdf) The pages 17, 19, 24, 27, and 28 are misplaced at the end of the pdf file!
  • I. Shimada and T. Nagashima, "A numerical approach to ergodic problem of dissipative dynamical system," Progress of Theoretical Physics 61 (6), 1605-1616 (1979) (pdf)