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Data-Driven Modeling & Scientific Computation : Methods for Complex Systems & Big Data

Author: Jose Nathan Kutz
Publisher: Oxford : Oxford University Press, 2013. ©2013
Edition/Format:   Print book : English : First editionView all editions and formats
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Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques  Read more...

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Document Type: Book
All Authors / Contributors: Jose Nathan Kutz
ISBN: 9780199660339 0199660336 9780199660346 0199660344
OCLC Number: 858608087
Language Note: Text in English.
Description: xvii, 638 pages : illustrations (some color) ; 26 cm
Contents: pt. I Basic Computations and Visualization --
1. MATLAB Introduction --
1.1. Vectors and Matrices --
1.2. Logic, Loops and Iterations --
1.3. Iteration: The Newton-Raphson Method --
1.4. Function Calls, Input/Output Interactions and Debugging --
1.5. Plotting and Importing/Exporting Data --
2. Linear Systems --
2.1. Direct Solution Methods for Ax = b --
2.2. Iterative Solution Methods for Ax = b --
2.3. Gradient (Steepest) Descent for Ax = b --
2.4. Eigenvalues, Eigenvectors and Solvability --
2.5. Eigenvalues and Eigenvectors for Face Recognition --
2.6. Nonlinear Systems --
3. Curve Fitting --
3.1. Least-Square Fitting Methods --
3.2. Polynomial Fits and Splines --
3.3. Data Fitting with MATLAB --
4. Numerical Differentiation and Integration --
4.1. Numerical Differentiation --
4.2. Numerical Integration --
4.3. Implementation of Differentiation and Integration --
5. Basic Optimization --
5.1. Unconstrained Optimization (Derivative-Free Methods). 5.2. Unconstrained Optimization (Derivative Methods) --
5.3. Linear Programming --
5.4. Simplex Method --
5.5. Genetic Algorithms --
6. Visualization --
6.1. Customizing Plots and Basic 2D Plotting --
6.2. More 2D and 3D Plotting --
6.3. Movies and Animations --
pt. II Differential and Partial Differential Equations --
7. Initial and Boundary Value Problems of Differential Equations --
7.1. Initial Value Problems: Euler, Runge-Kutta and Adams Methods --
7.2. Error Analysis for Time-Stepping Routines --
7.3. Advanced Time-Stepping Algorithms --
7.4. Boundary Value Problems: The Shooting Method --
7.5. Implementation of Shooting and Convergence Studies --
7.6. Boundary Value Problems: Direct Solve and Relaxation --
7.7. Implementing MATLAB for Boundary Value Problems --
7.8. Linear Operators and Computing Spectra --
8. Finite Difference Methods --
8.1. Finite Difference Discretization --
8.2. Advanced Iterative Solution Methods for Ax = b. 8.3. Fast Poisson Solvers: The Fourier Transform --
8.4.Comparison of Solution Techniques for Ax = b: Rules of Thumb --
8.5. Overcoming Computational Difficulties --
9. Time and Space Stepping Schemes: Method of Lines --
9.1. Basic Time-Stepping Schemes --
9.2. Time-Stepping Schemes: Explicit and Implicit Methods --
9.3. Stability Analysis --
9.4.Comparison of Time-Stepping Schemes --
9.5. Operator Splitting Techniques --
9.6. Optimizing Computational Performance: Rules of Thumb --
10. Spectral Methods --
10.1. Fast Fourier Transforms and Cosine/Sine Transform --
10.2. Chebychev Polynomials and Transform --
10.3. Spectral Method Implementation --
10.4. Pseudo-Spectral Techniques with Filtering --
10.5. Boundary Conditions and the Chebychev Transform --
10.6. Implementing the Chebychev Transform --
10.7.Computing Spectra: The Floquet-Fourier-Hill Method --
11. Finite Element Methods --
11.1. Finite Element Basis --
11.2. Discretizing with Finite Elements and Boundaries. 11.3. MATLAB for Partial Differential Equations --
11.4. MATLAB Partial Differential Equations Toolbox --
pt. III Computational Methods for Data Analysis --
12. Statistical Methods and Their Applications --
12.1. Basic Probability Concepts --
12.2. Random Variables and Statistical Concepts --
12.3. Hypothesis Testing and Statistical Significance --
13. Time-Frequency Analysis: Fourier Transforms and Wavelets --
13.1. Basics of Fourier Series and the Fourier Transform --
13.2. FFT Application: Radar Detection and Filtering --
13.3. FFT Application: Radar Detection and Averaging --
13.4. Time-Frequency Analysis: Windowed Fourier Transforms --
13.5. Time-Frequency Analysis and Wavelets --
13.6. Multi-Resolution Analysis and the Wavelet Basis --
13.7. Spectrograms and the Gabor Transform in MATLAB --
13.8. MATLAB Filter Design and Wavelet Toolboxes --
14. Image Processing and Analysis --
14.1. Basic Concepts and Analysis of Images. 14.2. Linear Filtering for Image Denoising --
14.3. Diffusion and Image Processing --
15. Linear Algebra and Singular Value Decomposition --
15.1. Basics of the Singular Value Decomposition (SVD) --
15.2. The SVD in Broader Context --
15.3. Introduction to Principal Component Analysis (PCA) --
15.4. Principal Components, Diagonalization and SVD --
15.5. Principal Components and Proper Orthogonal Modes --
15.6. Robust PCA --
16. Independent Component Analysis --
16.1. The Concept of Independent Components --
16.2. Image Separation Problem --
16.3. Image Separation and MATLAB --
17. Image Recognition: Basics of Machine Learning --
17.1. Recognizing Dogs and Cats --
17.2. The SVD and Linear Discrimination Analysis --
17.3. Implementing Cat/Dog Recognition in MATLAB --
18. Basics of Compressed Sensing --
18.1. Beyond Least-Square Fitting: The L1 Norm --
18.2. Signal Reconstruction and Circumventing Nyquist --
18.3. Data (Image) Reconstruction from Sparse Sampling. 19. Dimensionality Reduction for Partial Differential Equations --
19.1. Modal Expansion Techniques for PDEs --
19.2. PDE Dynamics in the Right (Best) Basis --
19.3. Global Normal Forms of Bifurcation Structures in PDEs --
19.4. The POD Method and Symmetries/Invariances --
19.5. POD Using Robust PCA --
20. Dynamic Mode Decomposition --
20.1. Theory of Dynamic Mode Decomposition (DMD) --
20.2. Dynamics of DMD Versus POD --
20.3. Applications of DMD --
21. Data Assimilation Methods --
21.1. Theory of Data Assimilation --
21.2. Data Assimilation, Sampling and Kalman Filtering --
21.3. Data Assimilation for the Lorenz Equation --
22. Equation-Free Modeling --
22.1. Multi-Scale Physics: An Equation-Free Approach --
22.2. Lifting and Restricting in Equation-Free Computing --
22.3. Equation-Free Space-Time Dynamics --
23.Complex Dynamical Systems: Combining Dimensionality Reduction, Compressive Sensing and Machine Learning --
23.1.Combining Data Methods for Complex Systems. 23.2. Implementing a Dynamical Systems Library --
23.3. Flow Around a Cylinder: A Prototypical Example --
pt. IV Scientific Applications --
24. Applications of Differential Equations and Boundary Value Problems --
24.1. Neuroscience and the Hodgkin-Huxley Model --
24.2. Celestial Mechanics and the Three-Body Problem --
24.3. Atmospheric Motion and the Lorenz Equations --
24.4. Quantum Mechanics --
24.5. Electromagnetic Waveguides --
25. Applications of Partial Differential Equations --
25.1. The Wave Equation --
25.2. Mode-Locked Lasers --
25.3. Bose-Elnstein Condensates --
25.4. Advection-Diffusion and Atmospheric Dynamics --
25.5. Introduction to Reaction-Diffusion Systems --
25.6. Steady State Flow Over an Airfoil --
26. Applications of Data Analysis --
26.1. Analyzing Music Scores and the Gabor Transform --
26.2. Image Denoising through Filtering and Diffusion --
26.3. Oscillating Mass and Dimensionality Reduction --
26.4. Music Genre Identification.
Other Titles: Data-Driven Modeling and Scientific Computation
Responsibility: J. Nathan Kutz, Department of Applied Mathematics, University of Washington.

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