The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Andrew J. Majda is the Morse Professor of Arts and Sciences at the Courant Institute of New York University.
Inhaltsangabe
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.
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.
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