Numerical recipes. The art of scientific computing. 3rd ed.

*(English)*Zbl 1132.65001
Cambridge: Cambridge University Press (ISBN 978-0-521-88068-8/hbk; 978-0-511-33239-5/ebook). xxi, 1235 p. (2007).

The third edition of Numerical Recipes (NR) appears fifteen years after the first volume with the same title NR in FORTRAN [Numerical recipes. The art of scientific computing. Cambridge etc.: Cambridge University Press (1986; Zbl 0587.65003)], NR in C [Numerical recipes in C. The art of scientific computing. Cambridge etc.: Cambridge University Press (1988; Zbl 0661.65001)]. During this period the four authors also published the second edition NR in FORTRAN [Numerical recipes in FORTRAN. The art of scientific computing. 2nd ed. Cambridge: Cambridge University Press (1992; Zbl 0778.65002)], NR in C [Numerical recipes in C. The art of scientific computing. 2nd ed. Cambridge: Univ. Press (1992; Zbl 0845.65001)]. Although the skeleton of the first edition has been preserved till now, the improvement of the material is equally visible at the theoretical level and in the source codes.

The third edition contains 22 chapters, as follows: 1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two-point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Less-numerical algorithms.

Compared to the second edition, the recent book brings a series of noticeable developments. Chapters 16 and 21 are new.

Chapter 1 is reorganized in accordance with the state of art presented by the book. Novel topics are considered in the following chapters: Chapter 3 (Interpolation on a scattered data in multidimensions, Laplace interpolation); Chapter 6 (Generalized Fermi-Dirac integrals, Inverse of the function xlog(x), Statistical functions); Chapter 7 (Completely hashing a large array, Deviates from other distributions, Multivariate normal deviates, Linear feedback shift registers, Hash tables and hash memories); Chapter 10 (Initially bracketing a minimum, Line methods in multidimensions, Linear programming: interior-point methods, Dynamic programming ); Chapter 11 (Real symmetric matrices, Real nonsymmetric matrices); Chapter 14 (Information-theoretic properties of distributions ); Chapter 15 (Markov chain Monte Carlo, Gaussian process regression); Chapter 17 (Stochastic simulation of chemical reaction networks); Chapter 20 (Spectral methods). In the third edition, over 100 routines are completely new, and many more have been upgraded. The C++ codes are commercially available via internet, or on CD-ROMs.

Starting with the first edition, by covering both mathematics and programming aspects, NR has aimed to represent an encyclopedic book for those interested in scientific computing. The attractive style of the text and the availability of the codes ensured the popularity of the previous editions and also recommend this recent volume to different categories of readers, more or less experienced in numerical computation.

The third edition contains 22 chapters, as follows: 1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two-point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Less-numerical algorithms.

Compared to the second edition, the recent book brings a series of noticeable developments. Chapters 16 and 21 are new.

Chapter 1 is reorganized in accordance with the state of art presented by the book. Novel topics are considered in the following chapters: Chapter 3 (Interpolation on a scattered data in multidimensions, Laplace interpolation); Chapter 6 (Generalized Fermi-Dirac integrals, Inverse of the function xlog(x), Statistical functions); Chapter 7 (Completely hashing a large array, Deviates from other distributions, Multivariate normal deviates, Linear feedback shift registers, Hash tables and hash memories); Chapter 10 (Initially bracketing a minimum, Line methods in multidimensions, Linear programming: interior-point methods, Dynamic programming ); Chapter 11 (Real symmetric matrices, Real nonsymmetric matrices); Chapter 14 (Information-theoretic properties of distributions ); Chapter 15 (Markov chain Monte Carlo, Gaussian process regression); Chapter 17 (Stochastic simulation of chemical reaction networks); Chapter 20 (Spectral methods). In the third edition, over 100 routines are completely new, and many more have been upgraded. The C++ codes are commercially available via internet, or on CD-ROMs.

Starting with the first edition, by covering both mathematics and programming aspects, NR has aimed to represent an encyclopedic book for those interested in scientific computing. The attractive style of the text and the availability of the codes ensured the popularity of the previous editions and also recommend this recent volume to different categories of readers, more or less experienced in numerical computation.

Reviewer: Octavian Pastravanu (Iaşi)

##### MSC:

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

65Dxx | Numerical approximation and computational geometry (primarily algorithms) |

65Fxx | Numerical linear algebra |

65Hxx | Nonlinear algebraic or transcendental equations |

65Lxx | Numerical methods for ordinary differential equations |

65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

65Nxx | Numerical methods for partial differential equations, boundary value problems |

15-04 | Software, source code, etc. for problems pertaining to linear algebra |

33-04 | Software, source code, etc. for problems pertaining to special functions |

34-04 | Software, source code, etc. for problems pertaining to ordinary differential equations |

35-04 | Software, source code, etc. for problems pertaining to partial differential equations |

41-04 | Software, source code, etc. for problems pertaining to approximations and expansions |

42-04 | Software, source code, etc. for problems pertaining to harmonic analysis on Euclidean spaces |

62-04 | Software, source code, etc. for problems pertaining to statistics |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

65C10 | Random number generation in numerical analysis |

65C99 | Probabilistic methods, stochastic differential equations |

65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |

65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |

65K05 | Numerical mathematical programming methods |

65T40 | Numerical methods for trigonometric approximation and interpolation |

68-04 | Software, source code, etc. for problems pertaining to computer science |

68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |

90-04 | Software, source code, etc. for problems pertaining to operations research and mathematical programming |

68W30 | Symbolic computation and algebraic computation |