Being familiar with python is necessary for this volume, but the concepts used are simple. The description of the numerical methods is complete, but a comparison of methods is not always present leaving an inexperienced analyst to wonder which method is the best for a given situation. Python is also not the most efficient language for numerical computation, but is a good linker and with cython it can become a viable option. Overall I recommend this book for learning numerical methods as you will not be tangled in the programming language, but learning numerical methods.
Author(s): Jaan Kiusalaas
Publisher: Cambridge University Press
Year: 2005
Language: English
Pages: 433
Contents......Page 6
Preface......Page 8
1.1 General Information......Page 10
1.2 Core Python......Page 13
1.3 Functions and Modules......Page 25
1.4 Mathematics Modules......Page 26
1.5 numarray Module......Page 28
1.6 Scoping of Variables......Page 32
1.7 Writing and Running Programs......Page 34
2.1 Introduction......Page 36
2.2 Gauss Elimination Method......Page 43
2.3 LU Decomposition Methods......Page 50
2.4 Symmetric and Banded Coefficient Matrices......Page 65
2.5 Pivoting......Page 76
∗2.6 Matrix Inversion......Page 91
∗2.7 Iterative Methods......Page 94
∗2.8 Other Methods......Page 110
3.1 Introduction......Page 112
3.2 Polynomial Interpolation......Page 113
3.3 Interpolation with Cubic Spline......Page 124
3.4 Least-Squares Fit......Page 134
3.5 Other Methods......Page 150
4.1 Introduction......Page 151
4.2 Incremental Search Method......Page 152
4.3 Method of Bisection......Page 154
4.4 Brent’s Method......Page 157
4.5 Newton–Raphson Method......Page 163
4.6 Systems of Equations......Page 167
∗4.7 Zeroes of Polynomials......Page 179
4.8 Other Methods......Page 188
5.1 Introduction......Page 190
5.2 Finite Difference Approximations......Page 191
5.3 Richardson Extrapolation......Page 196
5.4 Derivatives by Interpolation......Page 199
6.1 Introduction......Page 207
6.2 Newton–Cotes Formulas......Page 208
6.3 Romberg Integration......Page 216
6.4 Gaussian Integration......Page 225
∗6.5 Multiple Integrals......Page 242
7.1 Introduction......Page 257
7.2 Taylor Series Method......Page 258
7.3 Runge–Kutta Methods......Page 264
7.4 Stability and Stiffness......Page 281
7.5 Adaptive Runge–Kutta Method......Page 284
7.6 Bulirsch–Stoer Method......Page 292
7.7 Other Methods......Page 303
8.1 Introduction......Page 304
8.2 Shooting Method......Page 305
8.3 Finite Difference Method......Page 319
9.1 Introduction......Page 333
9.2 Jacobi Method......Page 335
9.3 Inverse Power and Power Methods......Page 352
9.4 Householder Reduction to Tridiagonal Form......Page 367
9.5 Eigenvalues of Symmetric Tridiagonal Matrices......Page 374
9.6 Other Methods......Page 389
10.1 Introduction......Page 390
10.2 Minimization Along a Line......Page 392
10.3 Conjugate Gradient Methods......Page 398
10.4 Other Methods......Page 416
Appendices......Page 418
Index......Page 428
