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Algorithms for Minimization Without Derivatives by Richard P Brent: New
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eBay-objectnummer:402896442011
Specificaties
- Objectstaat
- Book Title
- Algorithms for Minimization Without Derivatives
- Publication Date
- 2013-04-17
- Pages
- 206
- ISBN
- 9780486419985
Over dit product
Product Identifiers
Publisher
Dover Publications, Incorporated
ISBN-10
0486419983
ISBN-13
9780486419985
eBay Product ID (ePID)
1978004
Product Key Features
Number of Pages
208 Pages
Language
English
Publication Name
Algorithms for Minimization Without Derivatives
Subject
Functional Analysis, General, Algebra / General, Mathematical Analysis
Publication Year
2013
Type
Textbook
Subject Area
Mathematics
Series
Dover Books on Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
7.8 Oz
Item Length
8.5 in
Item Width
5.4 in
Additional Product Features
Intended Audience
College Audience
LCCN
2001-047459
Dewey Edition
18
Illustrated
Yes
Dewey Decimal
515/.33
Table Of Content
PREFACE TO DOVER EDITION PREFACE 1 INTRODUCTION AND SUMMARY 1.1 Introduction 1.2 Summary2 "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 error3 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 Summary4 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 procedures5 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 algorithm6 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 procedures7 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
Synopsis
This outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. None of the algorithms requires an evaluation of derivatives; all depend entirely on sequential function evaluation, a highly practical scenario in the frequent event of difficult-to-evaluate derivatives. Topics include the use of successive interpolation for finding simple zeros of a function and its derivatives; an algorithm with guaranteed convergence for finding a minimum of a function of one variation; global minimization given an upper bound on the second derivative; and a new algorithm for minimizing a function of several variables without calculating derivatives. Many numerical examples augment the text, along with a complete analysis of rate of convergence for most algorithms and error bounds that allow for the effect of rounding errors., Outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Includes many numerical examples, plus complete analysis of rate of convergence for most algorithms and error bounds that allow for the effect of rounding errors. 1973 edition., Outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. 1973 edition., Outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima.
LC Classification Number
QA402.5.B74 2001
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