LEADER 04831nam 2200469 a 450 001 9910741394303321 005 20221108050432.0 010 $a0-511-88998-4 035 $a(CKB)2550000001226794 035 $a(StDuBDS)AH13437157 035 $a(EXLCZ)992550000001226794 100 $a20051222d2006 uy 0 101 0 $aeng 135 $aur||||||||||| 200 10$aDynamic data assimilation$b[electronic resource] /$ea least squares approach /$fJohn M. Lewis, S. Lakshmivarahan, Sudarshan Dhall 210 $aCambridge $cCambridge University Press$d2006 215 $a1 online resource (xxii, 654p. ) $cill., map 225 1 $aEncyclopedia of mathematics and its applications ;$v104 300 $aFormerly CIP.$5Uk 320 $aIncludes bibliographical references and index. 327 $a1. 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. Optimisation: 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; 18. Data assimilation-static models: concepts and formulation; 19. Classical algorithms for data assimilation; 20. 3DVAR - a Bayesian formulation; 21. Spatial digital filters; 22. Dynamical data assimilation: the straight line problem; 23. First-order adjoint method: linear dynamics; 24. First-order adjoint method: nonlinear dynamics; 25. Second-order adjoint method; 26. The ADVAR problem: a statistical and a recursive view; 27. Linear filtering - Part I: Kalman filter; 28. Linear filtering-part II; 29. Nonlinear filtering; 30. Reduced rank filters; 31. Predictability: a stochastic view; 32. Predictability: a deterministic view; Bibliography; Index. 330 8 $aDynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to make predictions about how a complex physical system will behave.$bA basic one-stop reference for graduate students and researchers. Based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Chapters end with a section that provides pointers to the literature, and a set of exercises with instructive hints. 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. 410 0$aEncyclopedia of mathematics and its applications ;$v104. 517 $aDynamic data assimilation 606 $aSimulation methods 606 $aMathematical models 608 $aElectronic books.$2lcsh 615 0$aSimulation methods. 615 0$aMathematical models. 676 $a511.8 700 $aLewis$b J. M$01425031 701 $aLakshmivarahan$b S$0543455 701 $aDhall$b Sudarshan Kumar$f1937-$0771366 801 0$bStDuBDS 801 1$bStDuBDS 801 2$bUk 801 2$bStDuBDSZ 801 2$bUkPrAHLS 906 $aBOOK 912 $a9910741394303321 996 $aDynamic data assimilation$93555145 997 $aUNINA