Call number:
19/M 93.0387
;
AWI S3-94-0071
Type of Medium:
Monograph available for loan
Pages:
xxv, 963 S.
,
graph. Darst.
ISBN:
052143064X
Language:
English
Note:
Contents:
Preface to the Second Edition. -
Preface to the First Edition. -
Legal Matters. -
Computer Programs by Chapter and Section. -
1 Preliminaries. -
1.0 Introduction. -
1.1 Program Organization and Control Structures. -
1.2 Error, Accuracy, and Stability. -
2 Solution of Linear Algebraic Equations. -
2.0 Introduction. -
2.1 Gauss-Jordan Elimination. -
2.2 Gaussian Elimination with Backsubstitution. -
2.3 LU Decomposition and Its Applications. -
2.4 Tridiagonal and Band Diagonal Systems of Equations. -
2.5 Iterative Improvement of a Solution to Linear Equations. -
2.6 Singular Value Decomposition. -
2.7 Sparse Linear Systems. -
2.8 Vandermonde Matrices and Toeplitz Matrices. -
2.9 Cholesky Decomposition. -
2.10 QR Decomposition. -
2.11 Is Matrix Inversion an N3 Process?. -
3 Interpolation and Extrapolation. -
3.0 Introduction. -
3.1 Polynomial Interpolation and Extrapolation. -
3.2 Rational Function Interpolation and Extrapolation. -
3.3 Cubic Spline Interpolation. -
3.4 How to Search an Ordered Table. -
3.5 Coefficients of the Interpolating Polynomial. -
3.6 Interpolation in Two or More Dimensions. -
4 Integration of Functions. -
4.0 Introduction. -
4.1 Classical Formulas for Equally Spaced Abscissas. -
4.2 Elementary Algorithms. -
4.3 Romberg Integration. -
4.4 Improper Integrals. -
4.5 Gaussian Quadratures and Orthogonal Polynomials. -
4.6 Multidimensional Integrals. -
5 Evaluation of Functions. -
5.0 Introduction. -
5.1 Series and Their Convergence. -
5.2 Evaluation of Continued Fractions. -
5.3 Polynomials and Rational Functions. -
5.4 Complex Arithmetic. -
5.5 Recurrence Relations and Clenshaw's Recurrence Formula. -
5.6 Quadratic and Cubic Equations. -
5.7 Numerical Derivatives. -
5.8 Chebyshev Approximation. -
5.9 Derivatives or Integrals of a Chebyshev-approximated Function. -
5.10 Polynomial Approximation from Chebyshev Coefficients. -
5.11 Economization of Power Series. -
5.12 Pade Approximants. -
5.13 Rational Chebyshev Approximation. -
5.14 Evaluation of Functions by Path Integration. -
6 Special Functions. -
6.0 Introduction. -
6.1 Gamma Function, Beta Function, Factorials, Binomial Coefficients. -
6.2 Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function. -
6.3 Exponential Integrals. -
6.4 Incomplete Beta Function, Student's Distribution, F-Distribution, Cumulative Binomial Distribution. -
6.5 Bessel Functions of Integer Order. -
6.6 Modified Bessel Functions of Integer Order. -
6.7 Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions. -
6.8 Spherical Harmonics. -
6.9 Fresnel Integrals, Cosine and Sine Integrals. -
6.10 Dawson's Integral. -
6.11 Elliptic Integrals and Jacobian Elliptic Functions. -
6.12 Hypergeometric Functions. -
7 Random Numbers. -
7.0 Introduction. -
7.1 Uniform Deviates. -
7.2 Transformation Method: Exponential and Normal Deviates. -
7.3 Rejection Method: Gamma, Poisson, Binomial Deviates. -
7.4 Generation of Random Bits. -
7.5 Random Sequences Based on Data Encryption. -
7.6 Simple Monte Carlo Integration. -
7.7 Quasi- (that is, Sub-) Random Sequences. -
7.8 Adaptive and Recursive Monte Carlo Methods. -
8 Sorting. -
8.0 Introduction. -
8.1 Straight Insertion and Shell's Method. -
8.2 Quicksort. -
8.3 Heapsort. -
8.4 Indexing and Ranking. -
8.5 Selecting the Mth Largest. -
8.6 Determination of Equivalence Classes. -
9 Root Finding and Nonlinear Sets of Equations. -
9.0 Introduction. -
9.1 Bracketing and Bisection. -
9.2 Secant Method, False Position Method, and Ridders' Method. -
9.3 Van Wijngaarden-Dekker-Brent Method. -
9.4 Newton-Raphson Method Using Derivative. -
9.5 Roots of Polynomials. -
9.6 Newton-Raphson Method for Nonlinear Systems of Equations. -
9.7 Globally Convergent Methods for Nonlinear Systems of Equations. -
10 Minimization or Maximization of Functions. -
10.0 Introduction. -
10.1 Golden Section Search in One Dimension. -
10.2 Parabolic Interpolation and Brent's Method in One Dimension. -
10.3 One-Dimensional Search with First Derivatives. -
10.4 Downhill Simplex Method in Multidimensions. -
10.5 Direction Set (Powell's) Methods in Multidimensions. -
10.6 Conjugate Gradient Methods in Multidimensions. -
10.7 Variable Metric Methods in Multidimensions. -
10.8 Linear Programming and the Simplex Method. -
10.9 Simulated Annealing Methods. -
11 Eigensystems. -
11.0 Introduction. -
11.1 Jacobi Transformations of a Symmetric Matrix. -
11.2 Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and Householder Reductions. -
11.3 Eigenvalues and Eigenvectors of a Tridiagonal Matrix. -
11.4 Hermitian Matrices. -
11.5 Reduction of a General Matrix to Hessenberg Form. -
11.6 The QR Algorithm for Real Hessenberg Matrices. -
11.7 Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration. -
12 Fast Fourier Transform. -
12.0 Introduction. -
12.1 Fourier Transform of Discretely Sampled Data. -
12.2 Fast Fourier Transform (FFT). -
12.3 FFT of Real Functions, Sine and Cosine Transforms. -
12.4 FFT in Two or More Dimensions. -
12.5 Fourier Transforms of Real Data in Two and Three Dimensions. -
12.6 External Storage or Memory-Local FFTs. -
13 Fourier and Spectral Applications. -
13.0 Introduction. -
13.1 Convolution and Deconvolution Using the FFT. -
13.2 Correlation and Autocorrelation Using the FFT. -
13.3 Optimal (Wiener) Filtering with the FFT. -
13.4 Power Spectrum Estimation Using the FFT. -
13.5 Digital Filtering in the Time Domain. -
13.6 Linear Prediction and Linear Predictive Coding. -
13.7 Power Spectrum Estimation by the Maximum Entropy (All Poles) Method. -
13.8 Spectral Analysis of Unevenly Sampled Data. -
13.9 Computing Fourier Integrals Using the FFT. -
13.10 Wavelet Transforms. -
13.11 Numerical Use of the Sampling Theorem. -
14 Statistical Description of Data. -
14.0 Introduction. -
14.1 Moments of a Distribution: Mean, Variance, Skewness, and So Forth. -
14.2 Do Two Distributions Have the Same Means or Variances?. -
14.3 Are Two Distributions Different?. -
14.4 Contingency Table Analysis of Two Distributions. -
14.5 Linear Correlation. -
14.6 Nonparametric or Rank Correlation. -
14.7 Do Two-Dimensional Distributions Differ?. -
14.8 Savitzky-Golay Smoothing Filters. -
15 Modeling of Data. -
15.0 Introduction. -
15.1 Least Squares as a Maximum Likelihood Estimator. -
15.2 Fitting Data to a Straight Line. -
15.3 Straight-Line Data with Errors in Both Coordinates. -
15.4 General Linear Least Squares. -
15.5 Nonlinear Models. -
15.6 Confidence Limits on Estimated Model Parameters. -
15.7 Robust Estimation. -
16 Integration of Ordinary Differential Equations. -
16.0 Introduction. -
16.1 Runge-Kutta Method. -
16.2 Adaptive Stepsize Control for Runge-Kutta. -
16.3 Modified Midpoint Method. -
16.4 Richardson Extrapolation and the Bulirsch-Stoer Method. -
16.5 Second-Order Conservative Equations. -
16.6 Stiff Sets of Equations. -
16.7 Multistep, Multivalue, and Predictor-Corrector Methods. -
17 Two Point Boundary Value Problems. -
17.0 Introduction. -
17.1 The Shooting Method. -
17.2 Shooting to a Fitting Point. -
17.3 Relaxation Methods. -
17.4 A Worked Example: Spheroidal Harmonics. -
17.5 Automated Allocation of Mesh Points. -
17.6 Handling Internal Boundary Conditions or Singular Points. -
18 Integral Equations and Inverse Theory. -
18.0 Introduction. -
18.1 Fredholm Equations of the Second Kind. -
18.2 Volterra Equations. -
18.3 Integral Equations with Singular Kernels. -
18.4 Inverse Problems and the Use of A Priori Information. -
18.5 Linear Regularization Methods. -
18.6 Backus-Gilbert Method. -
18.7 Maximum Entropy Image Restoration. -
19 Partial Differential Equations. -
19.0 Introduction. -
19.1 Flux-Conservative Initial Value Problems. -
19.2 Diffusive Initial Value Problems. -
19.3 Initial Value Problems in Multidi
Location:
Reading room
Location:
Reading room
Branch Library:
GFZ Library
Branch Library:
AWI Library
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