## Numerical Recipes in FORTRAN Example Book: The Art of Scientific Computing, Volumes 1-2"Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests." "All this is in addition to material on such basic topics as: linear equations, interpolation and extrapolation, integration, nonlinear root-finding, eigensystems, ordinary differential equations, evaluation of functions, sorting, optimization, statistical description and modeling of data, and two-point boundary value problems."--BOOK JACKET. |

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### Contents

Preliminaries | 1 |

Linear Algebraic Equations | 5 |

Interpolation and Extrapolation | 31 |

Integration of Functions | 42 |

Evaluation of Functions | 56 |

Special Functions | 67 |

Random Numbers | 98 |

Sorting | 112 |

Fast Fourier Transform | 156 |

Fourier and Spectral Applications | 167 |

Statistical Description of Data | 177 |

Modeling of Data | 197 |

Ordinary Differential Equations | 210 |

Integral Equations and Inverse Theory | 224 |

Partial Differential Equations | 228 |

LessNumerical Algorithms | 233 |

Root Finding and Sets of Equations | 122 |

Minimization and Maximization of Functions | 133 |

Eigensystems | 147 |

### Common terms and phrases

11 continue 12 11 continue call 11 continue close(7 11 continue END 13 continue write Bessel Function calculates CHARACTER Chebyshev coefficients compared continue 12 continue continue do 12 continue END SUBROUTINE continue goto data sets data1 decomposition demonstration program deviation Diskette IBM distribution DOUBLE PRECISION driver for routine eigenvalues eigenvectors Elliptic Integral END REAL FUNCTION END Routine endif 11 continue equations error evaluation Example Book EXTERNAL func FORTRAN function values Gaussian goto 10 read(7 grid idum Incomplete gamma function input INTEGER i,j REAL INTEGER i,nval REAL INTEGER NP interpolation interval iterations Julian day linear method mglin NTERM Numerical Recipes nval write open(7,file='FNCVAL.DAT',status='OLD original array original matrix output PARAMETER polynomial Press RETURN problem QR decomposition random number REAL FUNCTION func(x REAL PI return END Right-hand side vector roots Sample program Solution vector sorted array sparse matrix STOP END subroutine tridiagonal tridiagonal matrix zero