Stable time filtering of strongly unstable spatially extended systems

Proceedings of the National Academy of Sciences of the United States of America

Volumn 103, Issue 20, 2006, Pages 7548-7553

  Grote, Marcus J ^a   Majda, Andrew J ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Courant Friedrichs Lewy condition; Kalman filter; Observability; Stable filter; Unstable finite differences

Indexed keywords

ACCURACY; ARTICLE; DIFFUSION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; THEORETICAL STUDY; THERMODYNAMICS;

MATHEMATICS; MODELS, THEORETICAL; TIME FACTORS;

EID: 33646747425     PISSN: 00278424     EISSN: None     Source Type: Journal    
DOI: 10.1073/pnas.0602385103     Document Type: Article

References (17)

1. Majda, A. & Wang, X. (2005) Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flow (Cambridge Univ. Press, New York).
2. Majda, A., Abramov, R. & Grote, M. J. (2005) Information Theory and Stochastics for Multi-Scale Nonlinear Systems (Am. Math. Soc., Providence, RI).
3. Berliner, L. M., Milliff, R. E. & Wikle, C. K. (2003) J. Geophys. Res. 108, 3104-3120.
4. Miller, R., Carter, E. & Blue, S. (1999) Tellus 51, 167-194.
5. Ghil, M. & Malanotte-Rizzoli, P. (1991) Adv. Geophys. 33, 141-266.
6. Todling, R. & Ghil, M. (1994) Mon. Weather Rev. 122, 183-204.
7. Anderson, J. L. (2001) Mon. Weather Rev. 129, 2884-2903.
8. Anderson, J. L. (2003) Mon. Weather Rev. 131, 634-642.
9. Farell, B. & Ioannou, P. (2001) J. Atmos. Sci. 58, 3666-3680.
10. Farell, B. & Ioannou, P. (2005) J. Atmos. Sci. 62, 460-475.
11. Ott, E., Hunt, B., Szunyogh, I., Zimin, A., Kostelich, E., Corrazza, M., Kalnay, E. & Yorke, J. (2004) Tellus 56A, 415-428.
12. Chui, C. K. & Chen, G. (1987) Kalman Filtering (Springer, Berlin).
13. Jazwinski, A, (1970) Stochastic Processes and Filtering Theory (Academic, New York).
14. Kiapio, J. & Somersalo, E. (2005) Statistical and Computational Inverse Problems (Springer, New York).
15. Richtmeyer, R. & Morton, K. W. (1967) Difference Methods for Initial-Value Problems (Wiley-Interscience, New York).
16. Chorin, A. & Krause, P. (2004) Proc. Natl. Acad. Sci. USA 101, 15013-15017.
17. Cohn, S. & Dee, D. (1988) SIAM J. Num. Anal. 25, 586-617.