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Algorithms for Minimization Without Derivatives,9780486419985

Algorithms for Minimization Without Derivatives

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ISBN13:

9780486419985

ISBN10:
0486419983
Format:
Paperback
Pub. Date:
4/17/2013
Publisher(s):
Dover Publications
List Price: $15.95
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Summary

Outstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Many numerical examples, along with complete analysis of rate of convergence for most of the algorithms and error bounds that allow for the effect of rounding errors.

Table of Contents

Preface to Dover Edition viii
Preface ix
Introduction and Summary
1(8)
Introduction
1(3)
Summary
4(5)
Some Useful Results on Taylor Series, Divided Differences, and Lagrange Interpolation
9(10)
Introduction
9(1)
Notation and definitions
10(1)
Truncated Taylor series
11(1)
Lagrange interpolation
12(1)
Divided differences
13(2)
Differentiating the error
15(4)
The Use of Successive Interpolation for Finding Simple Zeros of a Function and its Derivatives
19(28)
Introduction
19(2)
The definition of order
21(1)
Convergence to a zero
22(2)
Superlinear convergence
24(2)
Strict superlinear convergence
26(3)
The exact order of convergence
29(5)
Stronger results for q = 1 and 2
34(6)
Accelerating convergence
40(3)
Some numerical examples
43(2)
Summary
45(2)
An Algorithm with Guaranteed Convergence for Finding a Zero of a Function
47(14)
Introduction
47(1)
The Algorithm
48(5)
Convergence properties
53(1)
Practical tests
54(2)
Conclusion
56(2)
ALGOL 60 procedures
58(3)
An Algorithm with Guaranteed Convergence for Finding a Minimum of a Function of one Variable
61(20)
Introduction
61(2)
Fundamental limitations because of rounding errors
63(2)
Unimodality and δ-unimodality
65(7)
An algorithm analogous to Dekker's algorithm
72(3)
Convergence properties
75(1)
Practical tests
76(2)
Conclusion
78(1)
An ALGOL 60 procedure
79(2)
Global Minimization Given an Upper Bound on the Second Derivative
81(35)
Introduction
81(3)
The basic theorems
84(2)
An algorithm for global minimization
86(11)
The rate of convergence in some special cases
97(3)
A lower bound on the number of function evaluations required
100(3)
Practical tests
103(2)
Some extensions and generalizations
105(2)
An algorithm for global minimization of a function of several variables
107(4)
Summary and conclusions
111(1)
ALGOL 60 procedures
112(4)
A New Algorithm for Minimizing a Function of Several Variables Without Calculating Derivatives
116(53)
Introduction and survey of the literature
116(6)
The effect of rounding errors
122(2)
Powell's algorithm
124(4)
The main modification
128(4)
The resolution ridge problem
132(3)
Some further details
135(2)
Numerical results and comparison with other methods
137(17)
Conclusion
154(1)
An ALGOL W procedure and test program
155(14)
Bibliography 169(18)
Appendix: Fortran subroutines 187(6)
Index 193


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