An introduction to numerical methods and optimization techniques:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
North-Holland Publ. Co.
1978
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 293 S. |
| ISBN: | 0444002634 |
Internformat
MARC
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| 100 | 1 | |a Daniels, Richard W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to numerical methods and optimization techniques |
| 264 | 1 | |a New York u.a. |b North-Holland Publ. Co. |c 1978 | |
| 300 | |a XIII, 293 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Numerical analysis | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface xi
1. Introduction 1
1.1 Historical Background 1
1.2 Numerical Methods 1
1.3 Optimization Techniques 4
1.4 Computer Philosophy Used in the Text 4
1.5 Error Analysis 6
Problems 11
2. Solution of Linear Equations 15
2.1 Introduction 15
2.2 Cramer s Rule 16
2.3 The Matrix Solution 17
2.4 Gauss Elimination 19
2.5 Crout Reduction 29
2.6 Suggested Reading in Related Topics 36
Problems 38
3. Solutions for a Nonlinear Equation 43
3.1 Introduction 43
3.2 Iterative Procedures 44
3.3 Newton s Method 45
3.4 Quadratic Interpolation and Muller s Method 50
3.5 Bairstow s Method 57
3.6 Suggested Reading in Related Topics 64
Problems 67
4. Interpolation 71
4.1 Introduction 71
4.2 A Unique Solution 72
vil
Vlll Contents
4.3 The Normalized Variable 73
4.4 Some Useful Operators, A and E 74
4.5 Difference Tables 77
4.6 The Newton Gregory Polynomial 78
4.7 The Lagrange Polynomial 82
4.8 Inverse Interpolation 85
4.9 Introduction to Least Squares Data Fitting 86
4.10 Spline Functions 89
4.11 Fourier Series Applied to Interpolation 91
4.12 Suggested Reading in Related Topics 97
Problems 100
5. Differentiation 103
5.1 Introduction 103
5.2 Method of Interpolating Polynomials 104
5.3 Method of Undetermined Coefficients 107
5.4 Application of Interpolating Programs 111
Problems 113
6. Integration 115
6.1 Introduction 115
6.2 Trapezoidal Rule 116
6.3 Simpson s Rules 121
6.4 Examples 125
6.5 Romberg Prediction 127
6.6 Method of Undetermined Coefficients 129
6.7 Predictor and Corrector Equations 131
6.8 Gaussian Quadrature 134
6.9 Suggested Reading in Related Topics 137
Problems 139
7. Solution of Differential Equations 143
7.1 Introduction 143
7.2 Classification of Differential Equations 144
7.3 Euler Method 144
7.4 Stability Analysis 147
7.5 Modified Euler Method 151
7.6 Runge Kutta Method 153
Contents Ix
7.7 Adams Method and Automatic Error Control 156
7.8 Solution of Higher Order Differential Equations 163
7.9 Boundary Value Problems 169
7.10 Suggested Reading in Related Topics 172
Problems 174
8. Introduction to Optimization Theory 177
8.1 Preliminary Remarks 177
8.2 Formulation of Optimization Problems 179
8.3 Overview of Various Optimization Techniques 181
8.4 The Simplex Optimization Technique 183
8.5 Applications of Simplex 190
8.6 Test Functions 195
Problems 202
9. Gradient Techniques 205
9.1 Introduction 205
9.2 Quadratic Interpolation for a Specific Direction 206
9.3 The Gradient 208
9.4 The Steepest Descent Optimization Technique 211
9.5 Applications of Steepest Descent 220
9.6 The Fletcher Powell Optimization Technique 226
Problems 233
10. The Least pth Optimization Technique 237
10.1 Introduction 237
10.2 The Least Squares Algorithm 238
10.3 The Least pth Algorithm 242
10.4 A Least / th Program 244
10.5 Application to Least Squares Data Fitting 252
10.6 Chebyshev Approximations 256
Problems 263
11. Constrained Optimization Problems 265
11.1 Introduction 265
11.2 Active Constraints versus Inactive Constraints 266
11.3 Transformations 269
x Contents
11.4 Penalty Functions 276
11.5 Concluding Comments about Optimization Tech¬
niques 280
Problems 282
References 285
Answers to Selected Problems 287
Index 291
|
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| id | DE-604.BV002745218 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:00Z |
| institution | BVB |
| isbn | 0444002634 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001755261 |
| oclc_num | 3843457 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-824 DE-29T DE-706 DE-83 |
| physical | XIII, 293 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | North-Holland Publ. Co. |
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| spelling | Daniels, Richard W. Verfasser aut An introduction to numerical methods and optimization techniques New York u.a. North-Holland Publ. Co. 1978 XIII, 293 S. txt rdacontent n rdamedia nc rdacarrier Analyse numérique Optimisation mathématique Mathematical optimization Numerical analysis Optimierung (DE-588)4043664-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Optimierung (DE-588)4043664-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Daniels, Richard W. An introduction to numerical methods and optimization techniques Analyse numérique Optimisation mathématique Mathematical optimization Numerical analysis Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4128130-5 |
| title | An introduction to numerical methods and optimization techniques |
| title_auth | An introduction to numerical methods and optimization techniques |
| title_exact_search | An introduction to numerical methods and optimization techniques |
| title_full | An introduction to numerical methods and optimization techniques |
| title_fullStr | An introduction to numerical methods and optimization techniques |
| title_full_unstemmed | An introduction to numerical methods and optimization techniques |
| title_short | An introduction to numerical methods and optimization techniques |
| title_sort | an introduction to numerical methods and optimization techniques |
| topic | Analyse numérique Optimisation mathématique Mathematical optimization Numerical analysis Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Analyse numérique Optimisation mathématique Mathematical optimization Numerical analysis Optimierung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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