Nonlinear parameter estimation: an integrated system in BASIC
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
1987
|
| Schriftenreihe: | Statistics: textbooks and monographs
82 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 493 S. 1 Diskette |
| ISBN: | 0824778197 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface ill
Notation xlii
Chapter 1: Overview and Purpose 1
1 0 Beginnings 1
1 1 History and Motivations 1
1 2 Purposes 7
1 3 Classic Problems 12
1 4 Landmarks In Nonlinear Estimation Methods 15
1 5 Statistical Approaches 19
1 6 Software Approaches 23
1 7 Characterization of Problems 25
1 8 outline of Intentions 30
chapter 2: Examples of Nonlinear Parameter Estimation
Problems 33
2 0 Examples — An Overview 33
2 1 Growth and Decay Models 34
2 2 Equilibrium Models in Sciences and Engineering 42
2 3 Maximum Likelihood Estimation 44
2 4 Robust Estimation Techniques 45
vli
vill Contents
2 5 Constraints Introducing Nonlinearity 46
2 6 Loss Functions Which Are Sums of Squares 48
Chapter 3: Exploring the Problem 53
3 0 Overview — Properties of Problems 53
3 1 The Function and Its Scaling 54
3 2 Including Constraints 58
3 3 Scaling of Parameters and Data 62
3 4 Nonlinear Transformations 67
3 5 A Simple Example 68
3 6 A Framework for Parameter Estimation 72
3 7 Testing Derivative Calculations 73
3 8 Testing Residual and Jacobian Calculations 82
3 9 Initial Parameter Estimates 88
Chapter 4: Direct Search Methods 91
4 0 Overview Direct Search Methods 91
4 1 Motivations 91
4 2 Background 94
4 3 Implementation Details 95
Chapter 5: The Hooke and Jeeves Method 101
5 0 Overview — Hooke and Jeeves 101
5 1 The Hooke and Jeeves Source code 104
5 2 Use of the Hooke and Jeeves Method 108
Chapter 6: The Nelder Mead Polytope Method 113
6 0 Overview Nelder Mead 113
6 1 Nelder Mead Source code 123
6 2 Use of the Nelder Mead Method 130
Chapter 7: Minimization Using the Gradient 133
7 0 Overview — Gradient Minimization 133
7 1 Motivation and Characterization 134
7 2 Perspective 139
Content3 ix
7 3 Masks and Bounds 142
7 4 A General Parameter Step Algorithm 144
7 5 Finite Difference Approximation of the Gradient 145
Chapter 8: The Conjugate Gradients Method 149
8 0 Overview ~ Conjugate Gradients 149
8 1 Conjugate Gradient Source code 151
8 2 Use of the Conjugate Gradients Method 158
chapter 9: The Truncated Newton Method 163
9 0 Overview — Truncated Newton 163
9 1 Truncated Newton Source code 167
9 2 Use of the Truncated Newton Method 174
Chapter 10: The Variable Metric Method 179
10 0 Overview — Variable Metric 179
10 1 Variable Metric Source code 182
10 2 Use of the Variable Metric Method 189
Chapter 11: Methods for Sums of Squared Functions 193
11 0 Overview — Sums of Squared Functions 193
11 1 Popularity of Nonlinear Least Squares 195
11 2 Conversion of Problems to Sums of Squares 196
11 3 Diverse Approaches 199
11 4 The Levenberg Marquardt Nash Approach 203
11 5 Marquardt Source code 207
11 6 Use of the Marquardt Method 215
11 7 Other Approaches 218
11 8 Numerical Approximation of the Jacoblan 221
Chapter 12: Choosing an Approach and Method 225
12 0 The Choices Facing the User 225
12 1 Indicators for a Given Method 228
12 2 General Performance of Methods 231
x Contents
Chapter 13: Measures and Consequences of Nonlinearity 245
13 0 Overview — Consequences of Nonlinearity 245
13 1 Why Nonlinear Estimation Is Difficult 247
13 2 Measures of Nonlinearity 251
13 3 Convergence Tests and Restarts 253
13 4 Estimates of Parameter Dispersion 258
13 5 A General Post Solution Analysis 261
13 6 POSTGEN General Post Solution Analysis 263
13 7 POSTMRT a Jacobian Dispersion Estimate 268
13 8 POSTVM a Hessian Dispersion Estimate 274
13 9 RESSAVE Display of Residuals 279
Chapter 14: Difficult Problems 283
14 0 Some Difficult Problems 283
14 1 Mixtures of Exponentials 283
14 2 Constrained Problems with Awkward Feasible
Regions 291
14 3 Multiple Minima 293
14 4 Global Minima 299
14 5 The Variable Projection Method 302
Chapter 15: Implementation Details 305
15 0 Implementation Details 305
15 1 Block Structure 306
15 2 Main Driver Code 312
15 3 The Problem File 319
15 4 File Input / Output 325
15 5 Consolidation of Program Segments 327
15 6 Testing Functions and Derivatives 333
15 7 Plotting 335
Chapter 16: Examples from Chemical Kinetics 341
16 0 Chemical Kinetic Parameter Estimation Problems 341
Contents xl
16 1 The Michaelis Menten Curve 341
16 2 More Complicated Kinetic Models 345
16 3 A Simple Chemical Kinetics Example 352
16 4 The BMDP and Related Examples 355
16 5 Concurrent Chemical Reactions 358
Chapter 17: Applications in Economic Modeling and
Forecasting 365
17 0 Economic Modeling and Forecasting 365
17 1 Estimation of an Econometric Model 365
17 2 Simulation o£ Econometric Models 373
17 3 Production Functions 375
17 4 Forecasting Problems 380
Chapter 18: Test Problems and Other Examples 387
18 0 Test Problems and Other Examples 387
18 1 Simple Tests 387
18 2 Problems from S. G. Nash 392
18 3 WOODR.RES and WOOD.FN A Traditional Test 393
18 4 NASHEASY.FN A Large but Easy Problem 395
18 5 NASHHARD.FN A Large but Awkward Problem 395
18 6 LONION.RES A Yield Density Model Problem 396
18 7 RS.FN General Inequality Constraints 399
18 8 The Mor6, Garbow and Hillstrom Test Problems 402
Appendix A: Program Code for Test and Example Problems 405
ABS.FN 405
BAGLIVO.RES 406
BT.RES 407
CAL4.FN 407
GENROSE.FN 408
GENROSEJ.RES 410
KMENTALP.RES 411
LINTEST.RES 413
LONION.RES 414
xii Contents
NASHEASY.FN 417
NASHHARD.FN 418
QUADSN.FN 419
RS.FN 420
WOOD.FN 421
WOODR.RES 422
Appendix B: Data Dictionary 425
Appendix C: Line Number Conventions 435
Appendix D: Exceptions from Minimal BASIC in Code
Presented 437
Appendix E: Computing Environment 441
Bibliography 449
Author Index 481
Subject Index 485
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T15:19:17Z |
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| isbn | 0824778197 |
| language | English |
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| series2 | Statistics: textbooks and monographs |
| spelling | Nash, John C. 1947- Verfasser (DE-588)1045402818 aut Nonlinear parameter estimation an integrated system in BASIC John C. Nash ; Mary Walker-Smith New York [u.a.] Dekker 1987 XIII, 493 S. 1 Diskette txt rdacontent n rdamedia nc rdacarrier Statistics: textbooks and monographs 82 Datenverarbeitung BASIC (Computer program language) Parameter estimation Data processing BASIC (DE-588)4004624-2 gnd rswk-swf Programm (DE-588)4047394-6 gnd rswk-swf Nichtlineare Parameterschätzung gnd rswk-swf Nicht-lineare Parameterschätzung gnd rswk-swf Nichtlineare Parameterschätzung f BASIC (DE-588)4004624-2 s DE-604 Programm (DE-588)4047394-6 s Nicht-lineare Parameterschätzung f Walker-Smith, Mary Verfasser aut Statistics: textbooks and monographs 82 (DE-604)BV000003265 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000486704&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nash, John C. 1947- Walker-Smith, Mary Nonlinear parameter estimation an integrated system in BASIC Statistics: textbooks and monographs Datenverarbeitung BASIC (Computer program language) Parameter estimation Data processing BASIC (DE-588)4004624-2 gnd Programm (DE-588)4047394-6 gnd |
| subject_GND | (DE-588)4004624-2 (DE-588)4047394-6 |
| title | Nonlinear parameter estimation an integrated system in BASIC |
| title_auth | Nonlinear parameter estimation an integrated system in BASIC |
| title_exact_search | Nonlinear parameter estimation an integrated system in BASIC |
| title_full | Nonlinear parameter estimation an integrated system in BASIC John C. Nash ; Mary Walker-Smith |
| title_fullStr | Nonlinear parameter estimation an integrated system in BASIC John C. Nash ; Mary Walker-Smith |
| title_full_unstemmed | Nonlinear parameter estimation an integrated system in BASIC John C. Nash ; Mary Walker-Smith |
| title_short | Nonlinear parameter estimation |
| title_sort | nonlinear parameter estimation an integrated system in basic |
| title_sub | an integrated system in BASIC |
| topic | Datenverarbeitung BASIC (Computer program language) Parameter estimation Data processing BASIC (DE-588)4004624-2 gnd Programm (DE-588)4047394-6 gnd |
| topic_facet | Datenverarbeitung BASIC (Computer program language) Parameter estimation Data processing BASIC Programm Nichtlineare Parameterschätzung Nicht-lineare Parameterschätzung |
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