Filtering complex turbulent systems
By: Andrew J. Majda, John Harlim
Contributors: Harlim, John
Publisher: Cambridge University Press
Published: 2012
Place of publication: Cambridge; New York
Language: eng
Number of pages: 357
ISBN-13: 9781107016668
Subjects: Mathematical models; Dynamics; Filters (Mathematics); Numerical analysis; Turbulence
Notes: Includes bibliographical references (p. [350]-355) and index.
Table of contents: title: 1. Introduction and overview: mathematical strategies for filtering turbulent systems; title: 2. Filtering a stochastic complex scalar: the prototype test problem; title: 3. The Kalman filter for vector systems: reduced filters and a three-dimensional toy model; title: 4. Continuous and discrete Fourier series and numerical discretization; title: 5. Stochastic models for turbulence; title: 6. Filtering turbulent signals: plentiful observations; title: 7. Filtering turbulent signals: regularly spaced sparse observations; title: 8. Filtering linear stochastic PDE models with instability and model error; title: 9. Strategies for filtering nonlinear systems; title: 10. Filtering prototype nonlinear slow-fast systems; title: 11. Filtering turbulent nonlinear dynamical systems by finite ensemble methods; title: 12. Filtering turbulent nonlinear dynamical systems by linear stochastic models; title: 13. Stochastic parametrized extended Kalman filter for filtering turbulent signals with model error; title: 14. Filtering turbulent tracers from partial observations: an exactly solvable test model; title: 15. The search for efficient skillful particle filters for high-dimensional turbulent dynamical systems.