bookcpdf.html

C常用数值算法

<LI> <a href="bookcpdf/c9-4.pdf"><img src="PDF4.gif"></a> 9.4  Newton-Raphson Method Using Derivative  362

<LI> <a href="bookcpdf/c9-5.pdf"><img src="PDF4.gif"></a> 9.5  Roots of Polynomials  369

<LI> <a href="bookcpdf/c9-6.pdf"><img src="PDF4.gif"></a> 9.6  Newton-Raphson Method for Nonlinear Systems of Equations  379

<LI> <a href="bookcpdf/c9-7.pdf"><img src="PDF4.gif"></a> 9.7  Globally Convergent Methods for Nonlinear Systems of

Equations  383

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<h2> 10  Minimization or Maximization of Functions </h2>

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<LI> <a href="bookcpdf/c10-0.pdf"><img src="PDF4.gif"></a> 10.0  Introduction  394

<LI> <a href="bookcpdf/c10-1.pdf"><img src="PDF4.gif"></a> 10.1  Golden Section Search in One Dimension  397

<LI> <a href="bookcpdf/c10-2.pdf"><img src="PDF4.gif"></a> 10.2  Parabolic Interpolation and Brent's Method in One Dimension  402

<LI> <a href="bookcpdf/c10-3.pdf"><img src="PDF4.gif"></a> 10.3  One-Dimensional Search with First Derivatives  305

<LI> <a href="bookcpdf/c10-4.pdf"><img src="PDF4.gif"></a> 10.4  Downhill Simplex Method in Multidimensions  408

<LI> <a href="bookcpdf/c10-5.pdf"><img src="PDF4.gif"></a> 10.5  Direction Set (Powell's) Methods in Multidimensions  412

<LI> <a href="bookcpdf/c10-6.pdf"><img src="PDF4.gif"></a> 10.6  Conjugate Gradient Methods in Multidimensions  420

<LI> <a href="bookcpdf/c10-7.pdf"><img src="PDF4.gif"></a> 10.7  Variable Metric Methods in Multidimensions  425

<LI> <a href="bookcpdf/c10-8.pdf"><img src="PDF4.gif"></a> 10.8  Linear Programming and the Simplex Method  430

<LI> <a href="bookcpdf/c10-9.pdf"><img src="PDF4.gif"></a> 10.9  Simulated Annealing Methods  444

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<h2> 11  Eigensystems</h2>

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<LI> <a href="bookcpdf/c11-0.pdf"><img src="PDF4.gif"></a> 11.0  Introduction  456

<LI> <a href="bookcpdf/c11-1.pdf"><img src="PDF4.gif"></a> 11.1  Jacobi Transformations of a Symmetric Matrix  463

<LI> <a href="bookcpdf/c11-2.pdf"><img src="PDF4.gif"></a> 11.2  Reduction of a Symmetric Matrix to Tridiagonal Form:

Givens and Householder Reductions  469

<LI> <a href="bookcpdf/c11-3.pdf"><img src="PDF4.gif"></a> 11.3  Eigenvalues and Eigenvectors of a Tridiagonal Matrix  475

<LI> <a href="bookcpdf/c11-4.pdf"><img src="PDF4.gif"></a> 11.4  Hermitian Matrices  481

<LI> <a href="bookcpdf/c11-5.pdf"><img src="PDF4.gif"></a> 11.5  Reduction of a General Matrix to Hessenberg Form  482

<LI> <a href="bookcpdf/c11-6.pdf"><img src="PDF4.gif"></a> 11.6  The QR Algorithm for Real Hessenberg Matrices  486

<LI> <a href="bookcpdf/c11-7.pdf"><img src="PDF4.gif"></a> 11.7  Improving Eigenvalues and/or Finding Eigenvectors by

Inverse Iteration  493

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<h2> 12  Fast Fourier Transform</h2>

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<LI> <a href="bookcpdf/c12-0.pdf"><img src="PDF4.gif"></a> 12.0  Introduction  496

<LI> <a href="bookcpdf/c12-1.pdf"><img src="PDF4.gif"></a> 12.1  Fourier Transform of Discretely Sampled Data  500

<LI> <a href="bookcpdf/c12-2.pdf"><img src="PDF4.gif"></a> 12.2  Fast Fourier Transform (FFT)  504

<LI> <a href="bookcpdf/c12-3.pdf"><img src="PDF4.gif"></a> 12.3  FFT of Real Functions, Sine and Cosine Transforms  510

<LI> <a href="bookcpdf/c12-4.pdf"><img src="PDF4.gif"></a> 12.4  FFT in Two or More Dimensions  521

<LI> <a href="bookcpdf/c12-5.pdf"><img src="PDF4.gif"></a> 12.5  Fourier Transforms of Real Data in Two and Three Dimensions  525

<LI> <a href="bookcpdf/c12-6.pdf"><img src="PDF4.gif"></a> 12.6  External Storage or Memory-Local FFTs  532

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<h2> 13  Fourier and Spectral Applications</h2>

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<LI> <a href="bookcpdf/c13-0.pdf"><img src="PDF4.gif"></a> 13.0  Introduction  537

<LI> <a href="bookcpdf/c13-1.pdf"><img src="PDF4.gif"></a> 13.1  Convolution and Deconvolution Using the FFT  538

<LI> <a href="bookcpdf/c13-2.pdf"><img src="PDF4.gif"></a> 13.2  Correlation and Autocorrelation Using the FFT  545

<LI> <a href="bookcpdf/c13-3.pdf"><img src="PDF4.gif"></a> 13.3  Optimal (Wiener) Filtering with the FFT  547

<LI> <a href="bookcpdf/c13-4.pdf"><img src="PDF4.gif"></a> 13.4  Power Spectrum Estimation Using the FFT  549

<LI> <a href="bookcpdf/c13-5.pdf"><img src="PDF4.gif"></a> 13.5  Digital Filtering in the Time Domain  558

<LI> <a href="bookcpdf/c13-6.pdf"><img src="PDF4.gif"></a> 13.6  Linear Prediction and Linear Predictive Coding  564

<LI> <a href="bookcpdf/c13-7.pdf"><img src="PDF4.gif"></a> 13.7  Power Spectrum Estimation by the Maximum Entropy

(All Poles) Method  572

<LI> <a href="bookcpdf/c13-8.pdf"><img src="PDF4.gif"></a> 13.8  Spectral Analysis of Unevenly Sampled Data  575

<LI> <a href="bookcpdf/c13-9.pdf"><img src="PDF4.gif"></a> 13.9  Computing Fourier Integrals Using the FFT  584

<LI> <a href="bookcpdf/c13-10.pdf"><img src="PDF4.gif"></a> 13.10  Wavelet Transforms  591

<LI> <a href="bookcpdf/c13-11.pdf"><img src="PDF4.gif"></a> 13.11  Numerical Use of the Sampling Theorem  606

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<h2> 14  Statistical Description of Data </h2>

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<LI> <a href="bookcpdf/c14-0.pdf"><img src="PDF4.gif"></a> 14.0  Introduction  609

<LI> <a href="bookcpdf/c14-1.pdf"><img src="PDF4.gif"></a> 14.1  Moments of a Distribution:  Mean, Variance, Skewness,

and So Forth  610

<LI> <a href="bookcpdf/c14-2.pdf"><img src="PDF4.gif"></a> 14.2  Do Two Distributions Have the Same Means or Variances?  615

<LI> <a href="bookcpdf/c14-3.pdf"><img src="PDF4.gif"></a> 14.3  Are Two Distributions Different?  620

<LI> <a href="bookcpdf/c14-4.pdf"><img src="PDF4.gif"></a> 14.4  Contingency Table Analysis of Two Distributions  628

<LI> <a href="bookcpdf/c14-5.pdf"><img src="PDF4.gif"></a> 14.5  Linear Correlation  636

<LI> <a href="bookcpdf/c14-6.pdf"><img src="PDF4.gif"></a> 14.6  Nonparametric or Rank Correlation  639

<LI> <a href="bookcpdf/c14-7.pdf"><img src="PDF4.gif"></a> 14.7  Do Two-Dimensional Distributions Differ?  645

<LI> <a href="bookcpdf/c14-8.pdf"><img src="PDF4.gif"></a> 14.8  Savitzky-Golay Smoothing Filters  650

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<h2> 15  Modeling of Data </h2>

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<LI> <a href="bookcpdf/c15-0.pdf"><img src="PDF4.gif"></a> 15.0  Introduction  656

<LI> <a href="bookcpdf/c15-1.pdf"><img src="PDF4.gif"></a> 15.1  Least Squares as a Maximum Likelihood Estimator  657

<LI> <a href="bookcpdf/c15-2.pdf"><img src="PDF4.gif"></a> 15.2  Fitting Data to a Straight Line  661

<LI> <a href="bookcpdf/c15-3.pdf"><img src="PDF4.gif"></a> 15.3  Straight-Line Data with Errors in Both Coordinates  666

<LI> <a href="bookcpdf/c15-4.pdf"><img src="PDF4.gif"></a> 15.4  General Linear Least Squares  671

<LI> <a href="bookcpdf/c15-5.pdf"><img src="PDF4.gif"></a> 15.5  Nonlinear Models  681

<LI> <a href="bookcpdf/c15-6.pdf"><img src="PDF4.gif"></a> 15.6  Confidence Limits on Estimated Model Parameters  689

<LI> <a href="bookcpdf/c15-7.pdf"><img src="PDF4.gif"></a> 15.7  Robust Estimation  699

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<h2> 16  Integration of Ordinary Differential Equations </h2>

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<LI> <a href="bookcpdf/c16-0.pdf"><img src="PDF4.gif"></a> 16.0  Introduction  707

<LI> <a href="bookcpdf/c16-1.pdf"><img src="PDF4.gif"></a> 16.1  Runge-Kutta Method  710

<LI> <a href="bookcpdf/c16-2.pdf"><img src="PDF4.gif"></a> 16.2  Adaptive Stepsize Control for Runge-Kutta  714

<LI> <a href="bookcpdf/c16-3.pdf"><img src="PDF4.gif"></a> 16.3  Modified Midpoint Method  722

<LI> <a href="bookcpdf/c16-4.pdf"><img src="PDF4.gif"></a> 16.4  Richardson Extrapolation and the Bulirsch-Stoer Method  724

<LI> <a href="bookcpdf/c16-5.pdf"><img src="PDF4.gif"></a> 16.5  Second-Order Conservative Equations  732

<LI> <a href="bookcpdf/c16-6.pdf"><img src="PDF4.gif"></a> 16.6  Stiff Sets of Equations  734

<LI> <a href="bookcpdf/c16-7.pdf"><img src="PDF4.gif"></a> 16.7  Multistep, Multivalue, and Predictor-Corrector Methods  747

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<h2> 17  Two Point Boundary Value Problems </h2>

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<LI> <a href="bookcpdf/c17-0.pdf"><img src="PDF4.gif"></a> 17.0  Introduction  753

<LI> <a href="bookcpdf/c17-1.pdf"><img src="PDF4.gif"></a> 17.1  The Shooting Method  757

<LI> <a href="bookcpdf/c17-2.pdf"><img src="PDF4.gif"></a> 17.2  Shooting to a Fitting Point  760

<LI> <a href="bookcpdf/c17-3.pdf"><img src="PDF4.gif"></a> 17.3  Relaxation Methods  762

<LI> <a href="bookcpdf/c17-4.pdf"><img src="PDF4.gif"></a> 17.4  A Worked Example: Spheroidal Harmonics  772

<LI> <a href="bookcpdf/c17-5.pdf"><img src="PDF4.gif"></a> 17.5  Automated Allocation of Mesh Points  783

<LI> <a href="bookcpdf/c17-6.pdf"><img src="PDF4.gif"></a> 17.6  Handling Internal Boundary Conditions or Singular Points  784

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<h2> 18  Integral Equations and Inverse Theory </h2>

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<LI> <a href="bookcpdf/c18-0.pdf"><img src="PDF4.gif"></a> 18.0  Introduction  788

<LI> <a href="bookcpdf/c18-1.pdf"><img src="PDF4.gif"></a> 18.1  Fredholm Equations of the Second Kind  791

<LI> <a href="bookcpdf/c18-2.pdf"><img src="PDF4.gif"></a> 18.2  Volterra Equations  794

<LI> <a href="bookcpdf/c18-3.pdf"><img src="PDF4.gif"></a> 18.3  Integral Equations with Singular Kernels  797

<LI> <a href="bookcpdf/c18-4.pdf"><img src="PDF4.gif"></a> 18.4  Inverse Problems and the Use of A Priori Information  804

<LI> <a href="bookcpdf/c18-5.pdf"><img src="PDF4.gif"></a> 18.5  Linear Regularization Methods  808

<LI> <a href="bookcpdf/c18-6.pdf"><img src="PDF4.gif"></a> 18.6  Backus-Gilbert Method  815

<LI> <a href="bookcpdf/c18-7.pdf"><img src="PDF4.gif"></a> 18.7  Maximum Entropy Image Restoration  818

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<h2> 19  Partial Differential Equations </h2>

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<LI> <a href="bookcpdf/c19-0.pdf"><img src="PDF4.gif"></a> 19.0  Introduction  827

<LI> <a href="bookcpdf/c19-1.pdf"><img src="PDF4.gif"></a> 19.1  Flux-Conservative Initial Value Problems  834

<LI> <a href="bookcpdf/c19-2.pdf"><img src="PDF4.gif"></a> 19.2  Diffusive Initial Value Problems  847

<LI> <a href="bookcpdf/c19-3.pdf"><img src="PDF4.gif"></a> 19.3  Initial Value Problems in Multidimensions  853

<LI> <a href="bookcpdf/c19-4.pdf"><img src="PDF4.gif"></a> 19.4  Fourier and Cyclic Reduction Methods for Boundary

Value Problems  857

<LI> <a href="bookcpdf/c19-5.pdf"><img src="PDF4.gif"></a> 19.5  Relaxation Methods for Boundary Value Problems  863

<LI> <a href="bookcpdf/c19-6.pdf"><img src="PDF4.gif"></a> 19.6  Multigrid Methods for Boundary Value Problems  871

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<h2> 20  Less-Numerical Algorithms </h2>

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<LI> <a href="bookcpdf/c20-0.pdf"><img src="PDF4.gif"></a> 20.0  Introduction  889

<LI> <a href="bookcpdf/c20-1.pdf"><img src="PDF4.gif"></a> 20.1  Diagnosing Machine Parameters  889

<LI> <a href="bookcpdf/c20-2.pdf"><img src="PDF4.gif"></a> 20.2  Gray Codes  894

<LI> <a href="bookcpdf/c20-3.pdf"><img src="PDF4.gif"></a> 20.3  Cyclic Redundancy and Other Checksums  896

<LI> <a href="bookcpdf/c20-4.pdf"><img src="PDF4.gif"></a> 20.4  Huffman Coding and Compression of Data  903

<LI> <a href="bookcpdf/c20-5.pdf"><img src="PDF4.gif"></a> 20.5  Arithmetic Coding  910

<LI> <a href="bookcpdf/c20-6.pdf"><img src="PDF4.gif"></a> 20.6  Arithmetic at Arbitrary Precision  915

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<LI> <a href="bookcpdf/c21-1.pdf"><img src="PDF4.gif"></a> References and

Program Dependencies 926 

<LI> <a href="bookcpdf/c21-2.pdf"><img src="PDF4.gif"></a> General Index 965

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