Numerical Recipes in C
Acrobat ® Edition
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Front Matter, Contents, and Prefaces xi
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Legal Matters xvi
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Computer Programs by Chapter and Section xix
1. Preliminaries
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1.0 Introduction 1
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1.1 Program Organization and Control Structures 5
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1.2 Some C Conventions for Scientific Computing 15
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1.3 Error, Accuracy, and Stability 15
2. Solution of Linear Algebraic Equations
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2.0 Introduction 32
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2.1 Gauss-Jordan Elimination 36
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2.2 Gaussian Elimination with Backsubstitution 41
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2.3 LU Decomposition and Its Applications 43
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2.4 Tridiagonal and Band Diagonal Systems of Equations 50
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2.5 Iterative Improvement of a Solution to Linear Equations 55
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Numerical Recipes in C
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2.6 Singular Value Decomposition 59
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2.7 Sparse Linear Systems 71
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2.8 Vandermonde Matrices and Toeplitz Matrices 90
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2.9 Cholesky Decomposition 96
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2.10 QR Decomposition 98
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2.11 Is Matrix Inversion an $N^3$ Process? 102
3. Interpolation and Extrapolation
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3.0 Introduction 105
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3.1 Polynomial Interpolation and Extrapolation 108
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3.2 Rational Function Interpolation and Extrapolation 111
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3.3 Cubic Spline Interpolation 113
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3.4 How to Search an Ordered Table 117
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3.5 Coefficients of the Interpolating Polynomial 120
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3.6 Interpolation in Two or More Dimensions 123
4. Integration of Functions
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4.0 Introduction 129
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4.1 Classical Formulas for Equally Spaced Abscissas 130
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4.2 Elementary Algorithms 136
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4.3 Romberg Integration 140
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4.4 Improper Integrals 141
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4.5 Gaussian Quadratures and Orthogonal Polynomials 147
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4.6 Multidimensional Integrals 161
5. Evaluation of Functions