PREFACE TO DOVER EDITION |

PREFACE |

1 INTRODUCTION AND SUMMARY |

1.1 Introduction |

1.2 Summary |

2 "SOME USEFUL RESULTS ON TAYLOR SERIES, DIVIDED DIFFERENCIES, AND LAGRANGE INTERPOLATION" |

2.1 Introduction |

2.2 Notation and definitions |

2.3 Truncated Taylor series |

2.4 Lagrange interpolation |

2.5 Divided differences |

2.6 Differentiating the error |

3 THE USE OF SUCCESSIVE INTERPOLATION FOR FINDING SIMPLE ZEROS OF A FUNCTION AND ITS DERIVATIVES |

3.1 Introduction |

3.2 The definition of order |

3.3 Convergence to a zero |

3.4 Superlinear convergence |

3.5 Strict superlinear convergence |

3.6 The exact order of convergence |

3.7 Stronger results for q = 1 and 2 |

3.8 Accelerating convergence |

3.9 Some numerical examples |

3.10 Summary |

4 AN ALGORITHM WITH GUARANTEED CONVERGENCE FOR FINDING A ZERO OF A FUNCTION |

4.1 Introduction |

4.2 The algorithm |

4.3 Convergence properties |

4.4 Practical tests |

4.5 Conclusion |

4.6 ALGOL 60 procedures |

5 AN ALGORITHM WITH GUARANTEED CONVERGENCE FOR FINDING A MINIMUM OF A FUNCTION OF ONE VARIABLE |

5.1 Introduction |

5.2 Fundamental limitations because of rounding errors |

5.3 Unimodality and d-unimodality |

5.4 An algorithm analogous to Dekker's algorithm |

6 GLOBAL MINIMIZATION GIVEN AN UPPER BOUND ON THE SECOND DERIVATIVE |

6.1 Introduction |

6.2 The basic theorems |

6.3 An algorithm for global minimization |

6.4 The rate of convergence in some special cases |

6.5 A lower bound on the number of function evaluations required |

6.6 Practical tests |

6.7 Some extensions and generalizations |

6.8 An algorithm for global minimization of a function of several variables |

6.9 Summary and conclusions |

6.10 ALGOL 60 procedures |

7 A NEW ALGORITHM FOR MINIMIZING A FUNCTION OF SEVERAL VARIABLES WITHOUT CALCULATING DERIVATIVES |

7.1 Introduction and survey of the literature |

7.2 The effect of rounding errors |

7.3 Powell's algorithm |

7.4 The main modification |

7.5 The resolution ridge problem |

7.6 Some further details |

7.7 Numerical results and comparison with other methods |

7.8 Conclusion |

7.9 An ALGOL W procedure and test program |

BIBLIOGRAPHY |

APPENDIX: FORTRAN subroutines |

INDEX |