Page 8 - Applied Numerical Methods Using MATLAB

x CONTENTS
6.6 Boundary Value Problem (BVP) / 287
6.6.1 Shooting Method / 287
6.6.2 Finite Difference Method / 290
Problems / 293

7 Optimization 321

7.1 Unconstrained Optimization [L-2, Chapter 7] / 321
7.1.1 Golden Search Method / 321
7.1.2 Quadratic Approximation Method / 323
7.1.3 Nelder–Mead Method [ W-8] / 325
7.1.4 Steepest Descent Method / 328
7.1.5 Newton Method / 330
7.1.6 Conjugate Gradient Method / 332
7.1.7 Simulated Annealing Method [W-7] / 334
7.1.8 Genetic Algorithm [W-7] / 338
7.2 Constrained Optimization [L-2, Chapter 10] / 343
7.2.1 Lagrange Multiplier Method / 343
7.2.2 Penalty Function Method / 346
7.3 MATLAB Built-In Routines for Optimization / 350
7.3.1 Unconstrained Optimization / 350
7.3.2 Constrained Optimization / 352
7.3.3 Linear Programming (LP) / 355
Problems / 357

8 Matrices and Eigenvalues 371
8.1 Eigenvalues and Eigenvectors / 371
8.2 Similarity Transformation and Diagonalization / 373
8.3 Power Method / 378
8.3.1 Scaled Power Method / 378
8.3.2 Inverse Power Method / 380
8.3.3 Shifted Inverse Power Method / 380
8.4 Jacobi Method / 381
8.5 Physical Meaning of Eigenvalues/Eigenvectors / 385
8.6 Eigenvalue Equations / 389
Problems / 390

9 Partial Differential Equations 401

9.1 Elliptic PDE / 402
9.2 Parabolic PDE / 406
9.2.1 The Explicit Forward Euler Method / 406
9.2.2 The Implicit Backward Euler Method / 407