The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines bringing the total to well over 300, plus upgraded versions of the original routines, the new edition remains the most practical, comprehensive handbook of scientific computing available today.
Author(s): William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling
Edition: 2
Publisher: Cambridge University Press
Year: 1992
Language: English
Pages: 1018
Title......Page 1
Contents......Page 3
Preface......Page 9
List of Routines......Page 17
1. Preliminaries......Page 25
1.1 Program Structures......Page 29
1.2 C Conventions......Page 39
1.3 Accuracy and Stability......Page 52
2. Linear Algebra......Page 56
2.1 Gauss-Jordan Elimination......Page 60
2.2 Gaussian Elimination......Page 65
2.3 LU Decomposition......Page 67
2.4 Tridiagonal Systems......Page 74
2.5 Iterative Improvement......Page 79
2.6 Singular Value Decomposition......Page 83
2.7 Sparse Systems......Page 95
2.8 Vandermonde Matrices......Page 114
2.9 Cholesky Decomposition......Page 120
2.10 QR Decomposition......Page 122
2.11 Matrix Inversion......Page 126
3. Interpolation......Page 129
3.1 Polynomial Interpolation......Page 132
3.2 Rational Fcn Interpolation......Page 135
3.3 Cubic Spline Interpolation......Page 137
3.4 Ordered Table Searching......Page 141
3.5 Coeff's of Interpolating Poly......Page 144
3.6 Interpolation in N Dimensions......Page 147
4. Integration......Page 153
4.1 Classical Formulas......Page 154
4.2 Elementary Algorithms......Page 160
4.3 Romberg Integration......Page 164
4.4 Improper Integrals......Page 165
4.5 Gaussian Quadrature......Page 171
4.6 N-Dimensional Integrals......Page 185
5. Evaluating Functions......Page 189
6. Special Functions......Page 236
7. Random Numbers......Page 298
7.1 Uniform Deviates......Page 299
7.2 Transformation Method......Page 311
7.3 Rejection Method......Page 314
7.4 Random Bit Generation......Page 320
7.5 Random Sequences......Page 324
7.6 Monte Carlo Integration......Page 328
7.7 Quasi-Random Sequences......Page 333
7.8 Adaptive Monte Carlo......Page 340
8. Sorting......Page 353
9. Root Finding......Page 371
10. Minimization......Page 418
11. Eigensystems......Page 480
11.1 Jacobi Transformations......Page 487
11.2 Tridiagonal Reduction......Page 493
11.3 Tridiagonal Eigenvalues......Page 499
11.4 Hermitian Matrices......Page 505
11.5 Hessenberg Reduction......Page 506
11.6 QR for Hessenberg......Page 510
11.7 Inverse Iteration......Page 517
12. Fourier Transform......Page 520
13. Fourier Applications......Page 561
14. Statistics......Page 633
14.1 Distribution Moments......Page 634
14.2 Comparing Moments......Page 639
14.3 Comparing Distributions......Page 644
14.4 Contingency Analysis......Page 652
14.5 Linear Correlation......Page 660
14.6 Nonparametric Correlation......Page 663
14.7 Comparing 2D Distributions......Page 669
14.8 Smoothing Filters......Page 674
15. Modeling Data......Page 680
15.1 Least Squares......Page 681
15.2 Straight Line Fitting......Page 685
15.3 Straight Line Errors......Page 690
15.4 General Least Squares......Page 695
15.5 Nonlinear Models......Page 705
15.6 Confidence Limits......Page 713
15.7 Robust Estimation......Page 723
16. Ordinary Differential Eqns......Page 731
17. Boundary Value Problems......Page 777
18. Integral Equations......Page 812
19. Partial Differential Eqns......Page 851
20. Less Numerical Algorithms......Page 913
References......Page 950
A: Prototypes......Page 954
B: Utility Routines......Page 964
C: Complex Arithmetic......Page 972
Index of Routines......Page 975
Index......Page 989
