Page 14 - MATLAB an introduction with applications

Contents ——— xiii

4.7 Gauss-Jordan Method 204
4.8 Jacobi Method 205
4.9 The Householder Factorization 207
4.10 Symmetric Matrix Eigenvalue Problems 208
4.11 Jacobi Method 208
4.12 Householder Reduction to Tridiagonal Form 210
4.13 Sturn Sequence 211
4.14 QR Method 211
4.15 Example Problems and Solutions 214
References 254
Problems 259

5. OPTIMIZATION 261–318
5.1 Introduction 261
5.2 Conjugate Gradient Methods 261
5.3 Newton’s Method 262
5.4 The Concept of Quadratic Convergence 263
5.5 Powell’s Method 266
5.6 Fletcher-Reeves Method 267
5.7 Hooke and Jeeves Method 267
5.8 Interior Penalty Function Method 268
5.9 Example Problems and Solutions 270
References 316
Problems 316

6. DIRECT NUMERICAL INTEGRATION METHODS 319–387
6.1 Introduction 319
6.2 Single-degree of Freedom System 319
6.3 Multi-degree of Freedom System 322
6.4 Explicit Schemes 323
6.5 Implicit Schemes 328
6.6 Example Problems and Solutions 337
References 381
Problems 386
7. ENGINEERING MECHANICS 389–548
7.1 Introduction 389
7.2 Newtonian Mechanics 389
7.3 Newton’s Laws of Motion 389
7.4 Resultants of Coplanar Force Systems 390
7.5 Resultants of Non-coplanar Force Systems 391
7.6 Equilibrium of Coplanar Force Systems 392
7.7 Equilibrium of Non-coplanar Force System 394
7.8 Trusses 394