Data-driven modeling & scientific computation: methods for complex systems & big data

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methodswith data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from:· statistics, ·

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.…