Format:
1 Online-Ressource (xxii, 654 pages)
,
digital, PDF file(s).
ISBN:
9780511526480
Series Statement:
Encyclopedia of mathematics and its applications volume 104
Content:
Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. This book is designed to be a basic one-stop reference for graduate students and researchers. It is based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Thus Part I is a broad introduction to the history, development and philosophy of data assimilation, illustrated by examples; Part II considers the classical, static approaches, both linear and nonlinear; and Part III describes computational techniques. Parts IV to VII are concerned with how statistical and dynamic ideas can be incorporated into the classical framework. Key themes covered here include estimation theory, stochastic and dynamic models, and sequential filtering. The final part addresses the predictability of dynamical systems. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
1. Synopsis -- 2. Pathways into data assimilation : illustrative examples -- 3. Applications -- 4. Brief history of data assimilation -- 5. Linear least squares estimation : method of normal equations -- 6. A geometric view : projection and invariance -- 7. Nonlinear least squares estimation -- 8. Recursive least squares estimation -- 9. Matrix methods -- 10. Optimization : steepest descent method -- 11. Conjugate direction/gradient methods -- 12. Newton and quasi-Newton methods -- 13. Principles of statistical estimation -- 14. Statistical least squares estimation -- 15. Maximum likelihood method -- 16. Bayesian estimation method -- 17. From Gauss to Kalman : sequential, linear minimum variance estimation.
Additional Edition:
ISBN 9780521851558
Additional Edition:
ISBN 9780521851558
Additional Edition:
Erscheint auch als Lewis, John M. Dynamic data assimilation Cambridge[u.a.] : Cambridge University Press, 2006 ISBN 0521851556
Additional Edition:
ISBN 9780521851558
Additional Edition:
Print version ISBN 9780521851558
Language:
English
Subjects:
Mathematics
Keywords:
Daten
;
Simulation
;
Mathematisches Modell
;
Datenassimilation
;
Methode der kleinsten Quadrate
DOI:
10.1017/CBO9780511526480
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