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 |