## Numerical Methods that WorkNumerical Methods that Work, originally published in 1970, has been reissued by the MAA with a new preface and some additional problems. Acton deals with a commonsense approach to numerical algorithms for the solution of equations: algebraic, transcendental, and differential. He assumes that a computer is available for performing the bulk of the arithmetic. The book is divided into two parts, either of which could form the basis of a one-semester course in numerical methods. Part I discusses most of the standard techniques: roots of transcendental equations, roots of polynomials, eigenvalues of symmetric matrices, and so on. Part II cuts across the basic tools, stressing such commonplace problems as extrapolation, removal of singularities, and loss of significant figures. The book is written with clarity and precision, intended for practical rather than theoretical use. This book will interest mathematicians, both pure and applied, as well as any scientist or engineer working with numerical problems. |

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### Contents

THE CALCULATION OF FUNCTIONS | 5 |

ROOTS OF TRANSCENDENTAL EOUATIONS | 41 |

INTERPOLATION AND ALL THAT | 89 |

OUADRATURE | 100 |

ORDINARY DIFFERENTIAL EOUATIONS | 129 |

solved We then solve a slightly nonlinear differential equation | 134 |

ORDINARY DIFFERENTIAL EOUATIONS | 157 |

STRATEGY VERSUS TACTICS | 178 |

ECONOMIZATION OF APPROXIMATIONS | 289 |

EIGENVALUES IIROTATIONAL METHODS | 316 |

ROOTS OF EOUATIONSAGAIN | 361 |

THE CARE AND TREATMENT | 410 |

INSTABILITY IN EXTRAPOLATION | 431 |

MINIMUM METHODS | 448 |

An exposition of some of the more effective ways to find | 463 |

NETWORK PROBLEMS | 499 |

EIGENVALUES I | 204 |

FOURIER SERIES | 221 |

THE EVALUATION OF INTEGRALS | 261 |

POWER SERIES CONTINUED FRACTIONS | 279 |

AFTERTHOUGHTS | 529 |

BIBLIOGRAPHY | 537 |

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### Common terms and phrases

accuracy algebraic equations algorithm analytic approximation arguments arithmetic asymptotic asymptotic series automatic computer becomes calculation Chapter characteristic polynomial Chebyshev polynomial coefficients column complex constant continued fraction convergence correct cosine derivative diagonal differential equation difficulties direction efficient eigenvalues eigenvector equal error curve evaluate example exponential extrapolation extrema factor final finite Fourier Fourier series geometry give gradient grid hence Hessenberg infinite integral integrand interpolation iteration labor Laplace's equation linear matrix minimum multiple Newton's method node obtain ordinary differential equations origin orthogonal parabola parameters points positive power series precision predictor-corrector problem produce quadratic quadrature formulas rational function real roots recurrence replacement requires Runge–Kutta seek significant figures simple Simpson's rule singularity ſº solution solve standard step strategy subtraction symmetric tangent technique tion transformation tridiagonal form trouble unity usually variable vector zero