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<head><title>Numerical Recipes in C</title></head>

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<MENU>

<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>

<MENU>

<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



</MENU>

<h2> 2  Solution of Linear Algebraic Equations  </h2>

<MENU>

<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

</MENU>



<h2> 3  Interpolation and Extrapolation </h2>

<MENU>

<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

</MENU>



<h2> 4  Integration of Functions </h2>

<MENU>

<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

</MENU>



<h2> 5  Evaluation of Functions </h2>

<MENU>

<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

</MENU>



<h2> 6  Special Functions </h2>

<MENU>

<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

</MENU>



<h2> 7  Random Numbers</h2>

<MENU>

<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>

<MENU>

<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

</MENU>



<h2> 9  Root Finding and Nonlinear Sets of Equations</h2>

<MENU>

<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
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