Name: Filtering Complex Turbulent Systems By Andrew J. Majda (New York University)
SKU: 9781107016668
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Filtering Complex Turbulent Systems Summary

Filtering Complex Turbulent Systems by Andrew J. Majda (New York University)

Many natural phenomena ranging from climate through to biology are described by complex dynamical systems. Getting information about these phenomena involves filtering noisy data and prediction based on incomplete information (complicated by the sheer number of parameters involved), and often we need to do this in real time, for example for weather forecasting or pollution control. All this is further complicated by the sheer number of parameters involved leading to further problems associated with the 'curse of dimensionality' and the 'curse of small ensemble size'. The authors develop, for the first time in book form, a systematic perspective on all these issues from the standpoint of applied mathematics. The book contains enough background material from filtering, turbulence theory and numerical analysis to make the presentation self-contained and suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required to enlighten observations and models.

About Andrew J. Majda (New York University)

Andrew J. Majda is the Morse Professor of Arts and Sciences at the Courant Institute of New York University. John Harlim is Assistant Professor in the Department of Mathematics at North Carolina State University.

Preface; 1. Introduction and overview: mathematical strategies for filtering turbulent systems; Part I. Fundamentals: 2. Filtering a stochastic complex scalar: the prototype test problem; 3. The Kalman filter for vector systems: reduced filters and a three-dimensional toy model; 4. Continuous and discrete Fourier series and numerical discretization; Part II. Mathematical Guidelines for Filtering Turbulent Signals: 5. Stochastic models for turbulence; 6. Filtering turbulent signals: plentiful observations; 7. Filtering turbulent signals: regularly spaced sparse observations; 8. Filtering linear stochastic PDE models with instability and model error; Part III. Filtering Turbulent Nonlinear Dynamical Systems: 9. Strategies for filtering nonlinear systems; 10. Filtering prototype nonlinear slow-fast systems; 11. Filtering turbulent nonlinear dynamical systems by finite ensemble methods; 12. Filtering turbulent nonlinear dynamical systems by linear stochastic models; 13. Stochastic parameterized extended Kalman filter for filtering turbulent signal with model error; 14. Filtering turbulent tracers from partial observations: an exactly solvable test model; 15. The search for efficient skilful particle filters for high dimensional turbulent dynamical systems; References; Index.

Additional information

Sku

NPB9781107016668

ISBN 13

9781107016668

ISBN 10

1107016665

Title

Filtering Complex Turbulent Systems by Andrew J. Majda (New York University)

Author

Andrew J. Majda (New York University)

Condition

New

Binding type

Hardback

Publisher

Cambridge University Press

Year published

2012-02-23

Number of pages

368

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Filtering Complex Turbulent Systems Andrew J. Majda (New York University)

Filtering Complex Turbulent Systems by Andrew J. Majda (New York University)

Summary

Filtering Complex Turbulent Systems Summary

Filtering Complex Turbulent Systems by Andrew J. Majda (New York University)

About Andrew J. Majda (New York University)

Table of Contents

Additional information

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