Numerical Recipes in C. The Art of Scientific Computing

Автор(ы):William H. Press
06.10.2007
Год изд.:1992
Издание:2
Описание: Purpose in this book is to open up a large number of computational black boxes to your scrutiny. We want to teach you to take apart these black boxes and to put them back together again, modifying them to suit your specific needs. We assume that you are mathematically literate, i.e., that you have the normal mathematical preparation associated with an undergraduate degree in a physical science, or engineering, or economics, or a quantitative social science. We assume that you know how to program a computer. We do not assume that you have any prior formal knowledge of numerical analysis or numerical methods. The scope of Numerical Recipes is supposed to be "everything up to, but not including, partial differential equations." We honor this in the breach: First, we do have one introductory chapter on methods for partial differential equations (Chapter 19). Second, we obviously cannot include everything else. All the so-called "standard" topics of a numerical analysis course have been included in this book: linear equations (Chapter 2), interpolation and extrapolation (Chaper 3), integration (Chaper 4), nonlinear root-finding (Chapter 9), eigensystems (Chapter 11), and ordinary differential equations (Chapter 16). Most of these topics have been taken beyond their standard treatments into some advanced material which we have felt to be particularly important or useful.
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Numerical Recipes in C. The Art of Scientific Computing — обложка книги. Обложка книги.
1 Preliminaries [1]
  1.0 Introduction [1]
  1.1 Program Organization and Control Structures [5]
  1.2 Some С Conventions for Scientific Computing [15]
  1.3 Error, Accuracy, and Stability [28]
2 Solution of Linear Algebraic Equations [32]
  2.0 Introduction [32]
  2.1 Gauss-Jordan Elimination [36]
  2.2 Gaussian Elimination with Backsubstitution [41]
  2.3 LU Decomposition and Its Applications [43]
  2.4 Tridiagonal and Band Diagonal Systems of Equations [50]
  2.5 Iterative Improvement of a Solution to Linear Equations [55]
  2.6 Singular Value Decomposition [59]
  2.7 Sparse Linear Systems [71]
  2.8 Vandermonde Matrices and Toeplitz Matrices [90]
  2.9 Cholesky Decomposition [96]
  2.10 QR Decomposition [98]
  2.11 Is Matrix Inversion an N3 Process? [102]
3 Interpolation and Extrapolation [105]
  3.0 Introduction [105]
  3.1 Polynomial Interpolation and Extrapolation [108]
  3.2 Rational Function Interpolation and Extrapolation [111]
  3.3 Cubic Spline Interpolation [113]
  3.4 How to Search an Ordered Table [117]
  3.5 Coefficients of the Interpolating Polynomial [120]
  3.6 Interpolation in Two or More Dimensions [123]
4 Integration of Functions [129]
  4.0 Introduction [129]
  4.1 Classical Formulas for Equally Spaced Abscissas [130]
  4.2 Elementary Algorithms [136]
  4.3 Romberg Integration [140]
  4.4 Improper Integrals [141]
  4.5 Gaussian Quadratures and Orthogonal Polynomials [147]
  4.6 Multidimensional Integrals [161]
5 Evaluation of Functions [165]
  5.0 Introduction [165]
  5.1 Series and Their Convergence [165]
  5.2 Evaluation of Continued Fractions [169]
  5.3 Polynomials and Rational Functions [173]
  5.4 Complex Arithmetic [176]
  5.5 Recurrence Relations and Clenshaw's Recurrence Formula [178]
  5.6 Quadratic and Cubic Equations [183]
  5.7 Numerical Derivatives [186]
  5.8 Chebyshev Approximation [190]
  5.9 Derivatives or Integrals of a Chebyshev-approximated Function [195]
  5.10 Polynomial Approximation from Chebyshev Coefficients [197]
  5.11 Economization of Power Series [198]
  5.12 Fade Approximants [200]
  5.13 Rational Chebyshev Approximation [204]
  5.14 Evaluation of Functions by Path Integration [208]
6 Special Functions [212]
  6.0 Introduction [212]
  6.1 Gamma Function, Beta Function, Factorials, Binomial Coefficients [213]
  6.2 Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function [216]
  6.3 Exponential Integrals [222]
  6.4 Incomplete Beta Function, Student's Distribution, F-Distribution, Cumulative Binomial Distribution [226]
  6.5 Bessel Functions of Integer Order [230]
  6.6 Modified Bessel Functions of Integer Order [236]
  6.7 Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions [240]
  6.8 Spherical Harmonics [252]
  6.9 Fresnel Integrals, Cosine and Sine Integrals [255]
  6.10 Dawson's Integral [259]
  6.11 Elliptic Integrals and Jacobian Elliptic Functions [261]
  6.12 Hypergeometric Functions [271]
7 Random Numbers [274]
  7.0 Introduction [274]
  7.1 Uniform Deviates [275]
  7.2 Transformation Method: Exponential and Normal Deviates [287]
  7.3 Rejection Method: Gamma, Poisson, Binomial Deviates [290]
  7.4 Generation of Random В its [296]
  7.5 Random Sequences Based on Data Encryption [300]
  7.6 Simple Monte Carlo Integration [304]
  7.7 Quasi- (that is, Sub-) Random Sequences [309]
  7.8 Adaptive and Recursive Monte Carlo Methods [316]
8 Sorting [329]
  8.0 Introduction [329]
  8.1 Straight Insertion and Shell's Method [330]
  8.2 Quicksort [332]
  8.3 Heapsort [336]
  8.4 Indexing and Ranking [338]
  8.5 Selecting the Mm Largest [341]
  8.6 Determination of Equivalence Classes [345]
9 Root Finding and Nonlinear Sets of Equations [347]
  9.0 Introduction [347]
  9.1 Bracketing and Bisection [350]
  9.2 Secant Method, False Position Method, and Ridders' Method [354]
  9.3 Van Wijngaarden-Dekker-BrentMethod [359]
  9.4 Newton-Raphson Method Using Derivative [362]
  9.5 Roots of Polynomials [369]
  9.6 Newton-Raphson Method for Nonlinear Systems of Equations [379]
  9.7 Globally Convergent Methods for Nonlinear Systems of Equations [383]
10 Minimization or Maximization of Functions [394]
  10.0 Introduction [394]
  10.1 Golden Section Search in One Dimension [397]
  10.2 Parabolic Interpolation and Brent's Method in One Dimension [402]
  10.3 One-Dimensional Search with First Derivatives [405]
  10.4 Downhill Simplex Method in Multidimensions [408]
  10.5 Direction Set (Powell's) Methods in Multidimensions [412]
  10.6 Conjugate Gradient Methods in Multidimensions [420]
  10.7 Variable Metric Methods in Multidimensions [425]
  10.8 Linear Programming and the Simplex Method [430]
  10.9 Simulated Annealing Methods [444]
11 Eigensystems [456]
  11.0 Introduction [456]
  11.1 Jacobi Transformations of a Symmetric Matrix [463]
  11.2 Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and Householder Reductions [469]
  11.3 Eigenvalues and Eigenvectors of a Tridiagonal Matrix [475]
  11.4 Hermitian Matrices [481]
  11.5 Reduction of a General Matrix to Hessenberg Form [482]
  11.6 The QR Algorithm for Real Hessenberg Matrices [486]
  11.7 Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration [493]
12 Fast Fourier Transform [496]
  12.0 Introduction [496]
  12.1 Fourier Transform of Discretely Sampled Data [500]
  12.2 Fast Fourier Transform (FFT) [504]
  12.3 FFT of Real Functions, Sine and Cosine Transforms [510]
  12.4 FFT in Two or More Dimensions [521]
  12.5 Fourier Transforms of Real Data in Two and Three Dimensions [525]
  12.6 External Storage or Memory-Local FFTs [532]
13 Fourier and Spectral Applications [537]
  13.0 Introduction [537]
  13.1 Convolution and Deconvolution Using the FFT [538]
  13.2 Correlation and Autocorrelation Using the FFT [545]
  13.3 Optimal (Wiener) Filtering with the FFT [547]
  13.4 Power Spectrum Estimation Using the FFT [549]
  13.5 Digital Filtering in the Time Domain [558]
  13.6 Linear Prediction and Linear Predictive Coding [564]
  13.7 Power Spectrum Estimation by the Maximum Entropy (All Poles) Method [572]
  13.8 Spectral Analysis of Unevenly Sampled Data [575]
  13.9 Computing Fourier Integrals Using the FFT [584]
  13.10 Wavelet Transforms [591]
  13.11 Numerical Use of the Sampling Theorem [606]
14 Statistical Description of Data [609]
  14.0 Introduction [609]
  14.1 Moments of a Distribution: Mean, Variance, Skewness, and So Forth [610]
  14.2 Do Two Distributions Have the Same Means or Variances? [615]
  14.3 Are Two Distributions Different? [620]
  14.4 Contingency Table Analysis of Two Distributions [628]
  14.5 Linear Correlation [636]
  14.6 Nonparametric or Rank Correlation [639]
  14.7 Do Two-Dimensional Distributions Differ? [645]
  14.8 Savitzky-Golay Smoothing Filters [650]
15 Modeling of Data [656]
  15.0 Introduction [656]
  15.1 Least Squares as a Maximum Likelihood Estimator [657]
  15.2 Fitting Data to a Straight Line [661]
  15.3 Straight-Line Data with Errors in Both Coordinates [666]
  15.4 General Linear Least Squares [671]
  15.5 Nonlinear Models [681]
  15.6 Confidence Limits on Estimated Model Parameters [689]
  15.7 Robust Estimation [699]
16 Integration of Ordinary Differential Equations [707]
  16.0 Introduction [707]
  16.1 Runge-Kutta Method [710]
  16.2 Adaptive Stepsize Control for Runge-Kutta [714]
  16.3 Modified Midpoint Method [722]
  16.4 Richardson Extrapolation and the Bulirsch-Stoer Method [724]
  16.5 Second-Order Conservative Equations [732]
  16.6 Stiff Sets of Equations [734]
  16.7 Multistep, Multivalue, and Predictor-Corrector Methods [747]
17 Two Point Boundary Value Problems [753]
  17.0 Introduction [753]
  17.1 The Shooting Method [757]
  17.2 Shooting to a Fitting Point [760]
  17.3 Relaxation Methods [762]
  17.4 A Worked Example: Spheroidal Harmonics [772]
  17.5 Automated Allocation of Mesh Points [783]
  17.6 Handling Internal Boundary Conditions or Singular Points [784]
18 Integral Equations and Inverse Theory [788]
  18.0 Introduction [788]
  18.1 Fredholm Equations of the Second Kind [791]
  18.2 Volterra Equations [794]
  18.3 Integral Equations with Singular Kernels [797]
  18.4 Inverse Problems and the Use of A Priori Information [804]
  18.5 Linear Regularization Methods [808]
  18.6 Backus-Gilbert Method [815]
  18.7 Maximum Entropy Image Restoration [818]
19 Partial Differential Equations [827]
  19.0 Introduction [827]
  19.1 Flux-Conservative Initial Value Problems [834]
  19.2 Diffusive Initial Value Problems [847]
  19.3 Initial Value Problems in Multidimensions [853]
  19.4 Fourier and Cyclic Reduction Methods for Boundary Value Problems [857]
  19.5 Relaxation Methods for Boundary Value Problems [863]
  19.6 Multigrid Methods for В oundary Value Problems [871]
20 Less-Numerical Algorithms [889]
  20.0 Introduction [889]
  20.1 Diagnosing Machine Parameters [889]
  20.2 Gray Codes [894]
  20.3 Cyclic Redundancy and Other Checksums [896]
  20.4 Huffman Coding and Compression of Data [903]
  20.5 Arithmetic Coding [910]
  20.6 Arithmetic at Arbitrary Precision [915]
References [926]
Appendix A: Table of Prototype Declarations [930]
Appendix B: Utility Routines [940]
Appendix C: Complex Arithmetic [948]
Index of Programs and Dependencies [951]
General Index [965]
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Язык:ENG
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