Numerical methods and software. With disc.

*(English)*Zbl 0744.65002
Prentice Hall Series in Computational Mathematics. Englewood Cliffs, NJ: Prentice-Hall (ISBN 0-13-627258-4/hbk; 0-13-626672-X). xii, 495 p. (1989).

A major motivation for writing this text was to update and expand the material in the book by G. E. Forsythe, M. A. Malcolm, and the second author [Computer methods for mathematical computations (1977; Zbl 0361.65002)]. We liked its philosophy and informal style as well as the inclusion of programs. Our original intent was to produce a revision of that book but with Forsythe deceased and Malcolm involved in other activities the current authors decided to begin afresh. The publisher granted us permission to extract those portions of the original book that seemed appropriate. In practice this meant that several of the problems have been retained. The text is almost all new, although we were certainly inspired by the original. We would also like to acknowledge our debt to all those authors who have written on this subject before us; perhaps we may have made a few matters a little clearer or a little sounder. {From the preface}

Contents: 1. Introduction; 2. Computer arithmetic and computational errors; 3. Linear systems of equations; 4. Interpolation; 5. Numerical quadrature; 6. Linear least-squares data fitting; 7. Solutions of nonlinear equations; 8. Ordinary differential equations; 9. Optimization and nonlinear least squares; 10. Simulation and random numbers; 11. Trigonometric approximation and the fast Fourier transform.

Contents: 1. Introduction; 2. Computer arithmetic and computational errors; 3. Linear systems of equations; 4. Interpolation; 5. Numerical quadrature; 6. Linear least-squares data fitting; 7. Solutions of nonlinear equations; 8. Ordinary differential equations; 9. Optimization and nonlinear least squares; 10. Simulation and random numbers; 11. Trigonometric approximation and the fast Fourier transform.

##### MSC:

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

65Hxx | Nonlinear algebraic or transcendental equations |

65Lxx | Numerical methods for ordinary differential equations |

65Kxx | Numerical methods for mathematical programming, optimization and variational techniques |

65Cxx | Probabilistic methods, stochastic differential equations |

65Txx | Numerical methods in Fourier analysis |

65Fxx | Numerical linear algebra |

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