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Algorithms for Minimization Without Derivatives

Szerző: Richard P Brent

Nyelv:

Kötés: Puha kötésű

Kiadó: Dover Publications Inc.

Elérhetőség: Beszállítói készleten

Küldés 9-15 napon belül

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PREFACE TO DOVER EDITION PREFACE 1 INTRODUCTION AND SUMMARY 1.1 Introduction 1.2 Summary 2 "S...

Információk a könyvről

Szerző

Richard P Brent

Nyelv

Angol

Kötés

Könyv - Puha kötésű

Kiadva

2013

oldal

208

EAN

9780486419985

ISBN

0486419983

Enbook ID

01258428

Kiadó

Dover Publications Inc.

Súly

219

Méretek

136 x 214 x 10

Teljes leírás

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

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Algorithms for Minimization Without Derivatives

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