看到别人卖100个金币,太贵了,所以就上网找了半天终于让我找到了。我想也许也有人也需要这本书。
以下是目录
Preface to the Third Edition (2007) xi
Preface to the Second Edition (1992) xiv
Preface to the First Edition (1985) xvii
License and Legal Information xix
1 Preliminaries 1
1.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Error, Accuracy, and Stability . . . . . . . . . . . . . . . . . . . . 8
1.2 CFamilySyntax . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Objects,Classes, andInheritance . . . . . . . . . . . . . . . . . . 17
1.4 Vector andMatrixObjects . . . . . . . . . . . . . . . . . . . . . . 24
1.5 Some Further Conventions and Capabilities . . . . . . . . . . . . . 30
2 Solution of Linear Algebraic Equations 37
2.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.1 Gauss-JordanElimination . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Gaussian Elimination with Backsubstitution . . . . . . . . . . . . 46
2.3 LU Decomposition and Its Applications . . . . . . . . . . . . . . 48
2.4 Tridiagonal and Band-Diagonal Systems of Equations . . . . . . . 56
2.5 Iterative Improvementof aSolutiontoLinearEquations . . . . . . 61
2.6 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . 65
2.7 SparseLinearSystems . . . . . . . . . . . . . . . . . . . . . . . . 75
2.8 Vandermonde Matrices and Toeplitz Matrices . . . . . . . . . . . . 93
2.9 Cholesky Decomposition . . . . . . . . . . . . . . . . . . . . . . 100
2.10 QR Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.11 Is Matrix Inversion an N3 Process? . . . . . . . . . . . . . . . . . 106
3 Interpolation and Extrapolation 110
3.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.1 Preliminaries: Searching anOrderedTable . . . . . . . . . . . . . 114
3.2 Polynomial Interpolation and Extrapolation . . . . . . . . . . . . . 118
3.3 CubicSpline Interpolation . . . . . . . . . . . . . . . . . . . . . . 120
3.4 RationalFunctionInterpolationandExtrapolation . . . . . . . . . 124
3.5 Coefficients of the Interpolating Polynomial . . . . . . . . . . . . 129
3.6 Interpolation on a Grid in Multidimensions . . . . . . . . . . . . . 132
3.7 Interpolation on Scattered Data in Multidimensions . . . . . . . . 139
3.8 Laplace Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 150
4 Integration of Functions 155
4.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.1 Classical Formulas for Equally Spaced Abscissas . . . . . . . . . . 156
4.2 ElementaryAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 162
4.3 RombergIntegration . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.4 Improper Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 167
4.5 QuadraturebyVariableTransformation . . . . . . . . . . . . . . . 172
4.6 Gaussian Quadratures and Orthogonal Polynomials . . . . . . . . 179
4.7 AdaptiveQuadrature . . . . . . . . . . . . . . . . . . . . . . . . . 194
4.8 Multidimensional Integrals . . . . . . . . . . . . . . . . . . . . . 196
5 Evaluation of Functions 201
5.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.1 Polynomials and Rational Functions . . . . . . . . . . . . . . . . . 201
5.2 EvaluationofContinuedFractions . . . . . . . . . . . . . . . . . . 206
5.3 Series andTheirConvergence . . . . . . . . . . . . . . . . . . . . 209
5.4 Recurrence Relations and Clenshaw’s Recurrence Formula . . . . . 219
5.5 ComplexArithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 225
5.6 Quadratic andCubicEquations . . . . . . . . . . . . . . . . . . . 227
5.7 NumericalDerivatives . . . . . . . . . . . . . . . . . . . . . . . . 229
5.8 ChebyshevApproximation . . . . . . . . . . . . . . . . . . . . . . 233
5.9 Derivatives or Integrals of a Chebyshev-Approximated Function . . 240
5.10 Polynomial Approximation from Chebyshev Coefficients . . . . . 241
5.11 Economization of Power Series . . . . . . . . . . . . . . . . . . . 243
5.12 Pad´eApproximants . . . . . . . . . . . . . . . . . . . . . . . . . 245
5.13 RationalChebyshevApproximation . . . . . . . . . . . . . . . . . 247
5.14 EvaluationofFunctionsbyPathIntegration . . . . . . . . . . . . . 251
6 Special Functions 255
6.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
6.1 Gamma Function, Beta Function, Factorials, Binomial Coefficients 256
6.2 IncompleteGammaFunctionandErrorFunction . . . . . . . . . . 259
6.3 Exponential Integrals . . . . . . . . . . . . . . . . . . . . . . . . 266
6.4 IncompleteBetaFunction . . . . . . . . . . . . . . . . . . . . . . 270
6.5 BesselFunctionsof IntegerOrder . . . . . . . . . . . . . . . . . . 274
6.6 Bessel Functions of Fractional Order, Airy Functions, Spherical
BesselFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
6.7 SphericalHarmonics . . . . . . . . . . . . . . . . . . . . . . . . . 292
6.8 Fresnel Integrals,Cosine andSine Integrals . . . . . . . . . . . . . 297
6.9 Dawson’s Integral . . . . . . . . . . . . . . . . . . . . . . . . . . 302
6.10 GeneralizedFermi-Dirac Integrals . . . . . . . . . . . . . . . . . . 304
6.11 Inverse of the Function x log.x/ . . . . . . . . . . . . . . . . . . . 307
6.12 Elliptic Integrals and Jacobian Elliptic Functions . . . . . . . . . . 309
11 Eigensystems 563
11.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
11.1 JacobiTransformationsof aSymmetricMatrix . . . . . . . . . . . 570
11.2 RealSymmetricMatrices . . . . . . . . . . . . . . . . . . . . . . 576
11.3 Reduction of a Symmetric Matrix to Tridiagonal Form: Givens
andHouseholderReductions . . . . . . . . . . . . . . . . . . . . 578
11.4 Eigenvalues and Eigenvectors of a Tridiagonal Matrix . . . . . . . 583
11.5 Hermitian Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 590
11.6 RealNonsymmetricMatrices . . . . . . . . . . . . . . . . . . . . 590
11.7 The QRAlgorithmforRealHessenbergMatrices . . . . . . . . . 596
11.8 Improving Eigenvalues and/or Finding Eigenvectors by Inverse
Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597
12 Fast Fourier Transform 600
12.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
12.1 FourierTransformofDiscretelySampledData . . . . . . . . . . . 605
12.2 FastFourierTransform(FFT) . . . . . . . . . . . . . . . . . . . . 608
12.3 FFTofRealFunctions . . . . . . . . . . . . . . . . . . . . . . . . 617
12.4 FastSine andCosineTransforms . . . . . . . . . . . . . . . . . . 620
12.5 FFTinTwoorMoreDimensions . . . . . . . . . . . . . . . . . . 627
12.6 Fourier Transforms of Real Data in Two and Three Dimensions . . 631
12.7 ExternalStorage orMemory-LocalFFTs . . . . . . . . . . . . . . 637
13 Fourier and Spectral Applications 640
13.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
13.1 ConvolutionandDeconvolutionUsingtheFFT . . . . . . . . . . . 641
13.2 CorrelationandAutocorrelationUsingtheFFT . . . . . . . . . . . 648
13.3 Optimal (Wiener) Filtering with the FFT . . . . . . . . . . . . . . 649
13.4 PowerSpectrumEstimationUsingtheFFT . . . . . . . . . . . . . 652
13.5 Digital Filtering in the Time Domain . . . . . . . . . . . . . . . . 667
13.6 LinearPredictionandLinearPredictiveCoding . . . . . . . . . . . 673
13.7 Power Spectrum Estimation by the Maximum Entropy (All-Poles)
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
13.8 SpectralAnalysisofUnevenlySampledData . . . . . . . . . . . . 685
13.9 ComputingFourier IntegralsUsingtheFFT . . . . . . . . . . . . . 692
13.10 WaveletTransforms . . . . . . . . . . . . . . . . . . . . . . . . . 699
13.11 NumericalUse of theSamplingTheorem . . . . . . . . . . . . . . 717
14 Statistical Description of Data 720
14.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720
14.1 Moments of a Distribution: Mean, Variance, Skewness, and So Forth 721
14.2 Do Two Distributions Have the Same Means or Variances? . . . . . 726
14.3 AreTwoDistributionsDifferent? . . . . . . . . . . . . . . . . . . 730
14.4 ContingencyTableAnalysisofTwoDistributions . . . . . . . . . 741
14.5 LinearCorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . 745
14.6 Nonparametric or Rank Correlation . . . . . . . . . . . . . . . . . 748
14.7 Information-TheoreticPropertiesofDistributions . . . . . . . . . . 754
14.8 DoTwo-DimensionalDistributionsDiffer? . . . . . . . . . . . . . 762
14.9 Savitzky-Golay Smoothing Filters . . . . . . . . . . . . . . . . . . 766
15 Modeling of Data 773
15.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773
15.1 Least Squares as a Maximum Likelihood Estimator . . . . . . . . . 776
15.2 Fitting Data to a Straight Line . . . . . . . . . . . . . . . . . . . . 780
15.3 Straight-LineDatawithErrors inBothCoordinates . . . . . . . . 785
15.4 GeneralLinearLeastSquares . . . . . . . . . . . . . . . . . . . . 788
以下省略。。。。。
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