Dynamic data assimilation : a least squares approach / John M. Lewis, S. Lakshmivarahan, Sudarshan Dhall.

Format:

Book

Author/Creator:

Lewis, J. M., author.

Lakshmivarahan, S., author.

Dhall, Sudarshan Kumar, 1937- author.

Series:

Encyclopedia of mathematics and its applications ; v. 104.

Encyclopedia of mathematics and its applications ; volume 104

Language:

English

Subjects (All):

Simulation methods.

Mathematical models.

Physical Description:

1 online resource (xxii, 654 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2006.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 630-647) and index.

ISBN:

1-139-88323-2

1-107-38399-4

1-107-38750-7

1-107-39042-7

1-107-39883-5

0-511-52648-2

1-107-39522-4

OCLC:

668200904