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<head><title>Numerical Recipes in C</title></head>
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<LI> <a href="bookcpdf/c0-0.pdf"><img src="PDF4.gif"></a> Front Matter, Contents, and Prefaces xi
<LI> <a href="bookcpdf/c0-1.pdf"><img src="PDF4.gif"></a> Legal Matters xvi
<LI> <a href="bookcpdf/c0-2.pdf"><img src="PDF4.gif"></a> Computer Programs by Chapter and Section xix </MENU>
<h2> 1 Preliminaries </h2>
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<LI> <a href="bookcpdf/c1-0.pdf"><img src="PDF4.gif"></a> 1.0 Introduction 1
<LI> <a href="bookcpdf/c1-1.pdf"><img src="PDF4.gif"></a> 1.1 Program Organization and Control Structures 5
<LI> <a href="bookcpdf/c1-2.pdf"><img src="PDF4.gif"></a> 1.2 Some C Conventions for Scientific Computing 15
<LI> <a href="bookcpdf/c1-3.pdf"><img src="PDF4.gif"></a> 1.3 Error, Accuracy, and Stability 15
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<h2> 2 Solution of Linear Algebraic Equations </h2>
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<LI> <a href="bookcpdf/c2-0.pdf"><img src="PDF4.gif"></a> 2.0 Introduction 32
<LI> <a href="bookcpdf/c2-1.pdf"><img src="PDF4.gif"></a> 2.1 Gauss-Jordan Elimination 36
<LI> <a href="bookcpdf/c2-2.pdf"><img src="PDF4.gif"></a> 2.2 Gaussian Elimination with Backsubstitution 41
<LI> <a href="bookcpdf/c2-3.pdf"><img src="PDF4.gif"></a> 2.3 LU Decomposition and Its Applications 43
<LI> <a href="bookcpdf/c2-4.pdf"><img src="PDF4.gif"></a> 2.4 Tridiagonal and Band Diagonal Systems of Equations 50
<LI> <a href="bookcpdf/c2-5.pdf"><img src="PDF4.gif"></a> 2.5 Iterative Improvement of a Solution to Linear Equations 55
<LI> <a href="bookcpdf/c2-6.pdf"><img src="PDF4.gif"></a> 2.6 Singular Value Decomposition 59
<LI> <a href="bookcpdf/c2-7.pdf"><img src="PDF4.gif"></a> 2.7 Sparse Linear Systems 71
<LI> <a href="bookcpdf/c2-8.pdf"><img src="PDF4.gif"></a> 2.8 Vandermonde Matrices and Toeplitz Matrices 90
<LI> <a href="bookcpdf/c2-9.pdf"><img src="PDF4.gif"></a> 2.9 Cholesky Decomposition 96
<LI> <a href="bookcpdf/c2-10.pdf"><img src="PDF4.gif"></a> 2.10 QR Decomposition 98
<LI> <a href="bookcpdf/c2-11.pdf"><img src="PDF4.gif"></a> 2.11 Is Matrix Inversion an $N^3$ Process? 102
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<h2> 3 Interpolation and Extrapolation </h2>
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<LI> <a href="bookcpdf/c3-0.pdf"><img src="PDF4.gif"></a> 3.0 Introduction 105
<LI> <a href="bookcpdf/c3-1.pdf"><img src="PDF4.gif"></a> 3.1 Polynomial Interpolation and Extrapolation 108
<LI> <a href="bookcpdf/c3-2.pdf"><img src="PDF4.gif"></a> 3.2 Rational Function Interpolation and Extrapolation 111
<LI> <a href="bookcpdf/c3-3.pdf"><img src="PDF4.gif"></a> 3.3 Cubic Spline Interpolation 113
<LI> <a href="bookcpdf/c3-4.pdf"><img src="PDF4.gif"></a> 3.4 How to Search an Ordered Table 117
<LI> <a href="bookcpdf/c3-5.pdf"><img src="PDF4.gif"></a> 3.5 Coefficients of the Interpolating Polynomial 120
<LI> <a href="bookcpdf/c3-6.pdf"><img src="PDF4.gif"></a> 3.6 Interpolation in Two or More Dimensions 123
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<h2> 4 Integration of Functions </h2>
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<LI> <a href="bookcpdf/c4-0.pdf"><img src="PDF4.gif"></a> 4.0 Introduction 129
<LI> <a href="bookcpdf/c4-1.pdf"><img src="PDF4.gif"></a> 4.1 Classical Formulas for Equally Spaced Abscissas 130
<LI> <a href="bookcpdf/c4-2.pdf"><img src="PDF4.gif"></a> 4.2 Elementary Algorithms 136
<LI> <a href="bookcpdf/c4-3.pdf"><img src="PDF4.gif"></a> 4.3 Romberg Integration 140
<LI> <a href="bookcpdf/c4-4.pdf"><img src="PDF4.gif"></a> 4.4 Improper Integrals 141
<LI> <a href="bookcpdf/c4-5.pdf"><img src="PDF4.gif"></a> 4.5 Gaussian Quadratures and Orthogonal Polynomials 147
<LI> <a href="bookcpdf/c4-6.pdf"><img src="PDF4.gif"></a> 4.6 Multidimensional Integrals 161
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<h2> 5 Evaluation of Functions </h2>
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<LI> <a href="bookcpdf/c5-0.pdf"><img src="PDF4.gif"></a> 5.0 Introduction 165
<LI> <a href="bookcpdf/c5-1.pdf"><img src="PDF4.gif"></a> 5.1 Series and Their Convergence 165
<LI> <a href="bookcpdf/c5-2.pdf"><img src="PDF4.gif"></a> 5.2 Evaluation of Continued Fractions 169
<LI> <a href="bookcpdf/c5-3.pdf"><img src="PDF4.gif"></a> 5.3 Polynomials and Rational Functions 173
<LI> <a href="bookcpdf/c5-4.pdf"><img src="PDF4.gif"></a> 5.4 Complex Arithmetic 176
<LI> <a href="bookcpdf/c5-5.pdf"><img src="PDF4.gif"></a> 5.5 Recurrence Relations and Clenshaw's Recurrence Formula 178
<LI> <a href="bookcpdf/c5-6.pdf"><img src="PDF4.gif"></a> 5.6 Quadratic and Cubic Equations 183
<LI> <a href="bookcpdf/c5-7.pdf"><img src="PDF4.gif"></a> 5.7 Numerical Derivatives 186
<LI> <a href="bookcpdf/c5-8.pdf"><img src="PDF4.gif"></a> 5.8 Chebyshev Approximation 190
<LI> <a href="bookcpdf/c5-9.pdf"><img src="PDF4.gif"></a> 5.9 Derivatives or Integrals of a Chebyshev-approximated
Function 195
<LI> <a href="bookcpdf/c5-10.pdf"><img src="PDF4.gif"></a> 5.10 Polynomial Approximation from Chebyshev Coefficients 197
<LI> <a href="bookcpdf/c5-11.pdf"><img src="PDF4.gif"></a> 5.11 Economization of Power Series 198
<LI> <a href="bookcpdf/c5-12.pdf"><img src="PDF4.gif"></a> 5.12 Pad\'e Approximants 200
<LI> <a href="bookcpdf/c5-13.pdf"><img src="PDF4.gif"></a> 5.13 Rational Chebyshev Approximation 204
<LI> <a href="bookcpdf/c5-14.pdf"><img src="PDF4.gif"></a> 5.14 Evaluation of Functions by Path Integration 208
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<h2> 6 Special Functions </h2>
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<LI> <a href="bookcpdf/c6-0.pdf"><img src="PDF4.gif"></a> 6.0 Introduction 212
<LI> <a href="bookcpdf/c6-1.pdf"><img src="PDF4.gif"></a> 6.1 Gamma Function, Beta Function, Factorials, Binomial
Coefficients 213
<LI> <a href="bookcpdf/c6-2.pdf"><img src="PDF4.gif"></a> 6.2 Incomplete Gamma Function, Error Function, Chi-Square
Probability
Function, Cumulative Poisson Function 216
<LI> <a href="bookcpdf/c6-3.pdf"><img src="PDF4.gif"></a> 6.3 Exponential Integrals 222
<LI> <a href="bookcpdf/c6-4.pdf"><img src="PDF4.gif"></a> 6.4 Incomplete Beta Function, Student's Distribution,
F-Distribution,Cumulative Binomial Distribution 226
<LI> <a href="bookcpdf/c6-5.pdf"><img src="PDF4.gif"></a> 6.5 Bessel Functions of Integer Order 230
<LI> <a href="bookcpdf/c6-6.pdf"><img src="PDF4.gif"></a> 6.6 Modified Bessel Functions of Integer Order 236
<LI> <a href="bookcpdf/c6-7.pdf"><img src="PDF4.gif"></a> 6.7 Bessel Functions of Fractional Order, Airy Functions,
SphericalBessel Functions 240
<LI> <a href="bookcpdf/c6-8.pdf"><img src="PDF4.gif"></a> 6.8 Spherical Harmonics 252
<LI> <a href="bookcpdf/c6-9.pdf"><img src="PDF4.gif"></a> 6.9 Fresnel Integrals, Cosine and Sine Integrals 255
<LI> <a href="bookcpdf/c6-10.pdf"><img src="PDF4.gif"></a> 6.10 Dawson's Integral 259
<LI> <a href="bookcpdf/c6-11.pdf"><img src="PDF4.gif"></a> 6.11 Elliptic Integrals and Jacobian Elliptic Functions 261
<LI> <a href="bookcpdf/c6-12.pdf"><img src="PDF4.gif"></a> 6.12 Hypergeometric Functions 271
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<h2> 7 Random Numbers</h2>
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<LI> <a href="bookcpdf/c7-0.pdf"><img src="PDF4.gif"></a> 7.0 Introduction 274
<LI> <a href="bookcpdf/c7-1.pdf"><img src="PDF4.gif"></a> 7.1 Uniform Deviates 275
<LI> <a href="bookcpdf/c7-2.pdf"><img src="PDF4.gif"></a> 7.2 Transformation Method: Exponential and Normal Deviates 287
<LI> <a href="bookcpdf/c7-3.pdf"><img src="PDF4.gif"></a> 7.3 Rejection Method: Gamma, Poisson, Binomial Deviates 290
<LI> <a href="bookcpdf/c7-4.pdf"><img src="PDF4.gif"></a> 7.4 Generation of Random Bits 296
<LI> <a href="bookcpdf/c7-5.pdf"><img src="PDF4.gif"></a> 7.5 Random Sequences Based on Data Encryption 300
<LI> <a href="bookcpdf/c7-6.pdf"><img src="PDF4.gif"></a> 7.6 Simple Monte Carlo Integration 304
<LI> <a href="bookcpdf/c7-7.pdf"><img src="PDF4.gif"></a> 7.7 Quasi- (that is, Sub-) Random Sequences 309
<LI> <a href="bookcpdf/c7-8.pdf"><img src="PDF4.gif"></a> 7.8 Adaptive and Recursive Monte Carlo Methods 316
</MENU>
<h2> 8 Sorting </h2>
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<LI> <a href="bookcpdf/c8-0.pdf"><img src="PDF4.gif"></a> 8.0 Introduction 329
<LI> <a href="bookcpdf/c8-1.pdf"><img src="PDF4.gif"></a> 8.1 Straight Insertion and Shell's Method 330
<LI> <a href="bookcpdf/c8-2.pdf"><img src="PDF4.gif"></a> 8.2 Quicksort 332
<LI> <a href="bookcpdf/c8-3.pdf"><img src="PDF4.gif"></a> 8.3 Heapsort 336
<LI> <a href="bookcpdf/c8-4.pdf"><img src="PDF4.gif"></a> 8.4 Indexing and Ranking 338
<LI> <a href="bookcpdf/c8-5.pdf"><img src="PDF4.gif"></a> 8.5 Selecting the $M$th Largest 341
<LI> <a href="bookcpdf/c8-6.pdf"><img src="PDF4.gif"></a> 8.6 Determination of Equivalence Classes 345
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<h2> 9 Root Finding and Nonlinear Sets of Equations</h2>
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<LI> <a href="bookcpdf/c9-0.pdf"><img src="PDF4.gif"></a> 9.0 Introduction 347
<LI> <a href="bookcpdf/c9-1.pdf"><img src="PDF4.gif"></a> 9.1 Bracketing and Bisection 350
<LI> <a href="bookcpdf/c9-2.pdf"><img src="PDF4.gif"></a> 9.2 Secant Method, False Position Method, and Ridders' Method 354
<LI> <a href="bookcpdf/c9-3.pdf"><img src="PDF4.gif"></a> 9.3 Van Wijngaarden--Dekker--Brent Method 359
<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
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