Numerical data fitting in dynamical systems: a practical introduction with applications and software
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Kluwer Academic Publishers
2002
|
| Schriftenreihe: | Applied optimization
77 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index. - CD-ROM u.d.T.: Easy fit |
| Beschreibung: | XII, 392 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1402010796 |
Internformat
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Datensatz im Suchindex
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| adam_text | IMAGE 1
NUMERICAL DATA FITTING IN
DYNAMICAL SYSTEMS A PRACTICAL INTRODUCTION WITH APPLICATIONS AND
SOFTWARE
BY KLAUS SCHITTKOWSKI
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF BAYREUTH, BAYREUTH, GERMANY
**
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE XI
1. INTRODUCTION 1
2. MATHEMATICAL FOUNDATIONS 7
1 OPTIMALITY CRITERIA 7
1.1 NOTATION 7
1.2 CONVEXITY AND CONSTRAINT QUALIFICATION 9
1.3 NECESSARY AND SUFFICIENT OPTIMALITY CRITERIA 10
2 SEQUENTIAL QUADRATIC PROGRAMMING METHODS 14
2.1 THE QUADRATIC PROGRAMMING SUBPROBLEM 14
2.2 LINE SEARCH AND QUASI-NEWTON UPDATES 16
2.3 CONVERGENCE 18
2.4 SYSTEMS OF NONLINEAR EQUATIONS 20
3 LEAST SQUARES METHODS 23
3.1 OPTIMALITY CONDITIONS 23
3.2 GAUSS-NEWTON AND RELATED METHODS 24
3.3 SOLUTION OF LEAST SQUARES PROBLEMS BY SQP METHODS 27
3.4 CONSTRAINED LEAST SQUARES OPTIMIZATION 31
3.5 ALTERNATIVE NORMS 33
4 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS 38
4.1 EXPLICIT SOLUTION METHODS 38
4.2 IMPLICIT SOLUTION METHODS 40
4.3 SENSITIVITY EQUATIONS 43
4.4 INTERNAL NUMERICAL DIFFERENTIATION 46
5 NUMERICAL SOLUTION OF DIFFERENTIAL ALGEBRAIC EQUATIONS 48
5.1 ALGEBRAIC EQUATIONS 48
5.2 INDEX OF A DIFFERENTIAL ALGEBRAIC EQUATION 50
5.3 INDEX REDUCTION AND DRIFT EFFECT 52
5.4 PROJECTION METHODS 55
IMAGE 3
V1U
NUMERICAL DATA FITTING IN DYNAMICAL SYSTEMS
5.5 CONSISTENT INITIAL VALUES 60
5.6 IMPLICIT SOLUTION METHODS 62
6 NUMERICAL SOLUTION OF ONE-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS
66
6.1 THE GENERAL TIME-DEPENDENT MODEL 66
6.2 SOME SPECIAL CLASSES OF EQUATIONS 68
6.3 THE METHOD OF LINES 74
6.4 PARTIAL DIFFERENTIAL ALGEBRAIC EQUATIONS 78
6.5 DIFFERENCE FORMULAE 81
6.6 POLYNOMIAL INTERPOLATION 84
6.7 UPWIND FORMULAE FOR HYPERBOLIC EQUATIONS 85
6.8 ESSENTIALLY NON-OSCILLATORY SCHEMES 93
6.9 SYSTEMS OF HYPERBOLIC EQUATIONS 98
6.10 SENSITIVITY EQUATIONS 101
7 LAPLACE TRANSFORMS 104
7.1 BASIC PROPERTIES 104
7.2 NUMERICAL BACK-TRANSFORMATION 107
8 AUTOMATIC DIFFERENTIATION 109
8.1 FORWARD MODE 109
8.2 REVERSE MODE 112
9 STATISTICAL INTERPRETATION OF RESULTS 115
3. DATA FITTING MODELS 119
1 EXPLICIT MODEL FUNCTIONS 120
2 LAPLACE TRANSFORMS 124
3 STEADY STATE EQUATIONS 126
4 ORDINARY DIFFERENTIAL EQUATIONS 128
4.1 STANDARD FORMULATION 128
4.2 DIFFERENTIAL ALGEBRAIC EQUATIONS 129
4.3 SWITCHING POINTS 131
4.4 CONSTRAINTS 137
4.5 SHOOTING METHOD 141
4.6 BOUNDARY VALUE PROBLEMS 146
4.7 VARIABLE INITIAL TIMES 148
5 PARTIAL DIFFERENTIAL EQUATIONS 151
5.1 STANDARD FORMULATION 151
5.2 PARTIAL DIFFERENTIAL ALGEBRAIC EQUATIONS 153
5.3 FLUX FUNCTIONS 154
5.4 COUPLED ORDINARY DIFFERENTIAL ALGEBRAIC EQUATIONS 157
5.5 INTEGRATION AREAS AND TRANSITION CONDITIONS 162
5.6 SWITCHING POINTS 167
IMAGE 4
CONTENTS
IX
5.7 CONSTRAINTS 169
6 OPTIMAL CONTROL PROBLEMS 175
4. NUMERICAL EXPERIMENTS 181
1 TEST ENVIRONMENT 182
2 NUMERICAL PITFALLS 183
2.1 LOCAL SOLUTIONS 183
2.2 SLOW CONVERGENCE 186
2.3 BADLY SCALED DATA AND PARAMETERS 189
2.4 NON-IDENTIFIABILITY OF MODELS 192
2.5 ERRORS IN EXPERIMENTAL DATA 195
2.6 INCONSISTENT CONSTRAINTS 197
2.7 NON-DIFFERENTIABLE MODEL FUNCTIONS 201
2.8 OSCILLATING MODEL FUNCTIONS 205
3 TESTING THE VALIDITY OF MODELS 208
3.1 MASS BALANCE AND STEADY STATE ANALYSIS 208
3.2 STATISTICAL ANALYSIS 210
3.3 CONSTRAINTS 212
4 PERFORMANCE EVALUATION 216
4.1 COMPARING LEAST SQUARES ALGORITHMS 216
4.2 INDIVIDUAL NUMERICAL RESULTS 218
5. CASESTUDIES 231
1 LINEAR PHARMACOKINETICS 231
2 RECEPTOR-LIGAND BINDING STUDY 236
3 ROBOT DESIGN 239
4 MULTIBODY SYSTEM OF A TRACK 243
5 BINARY DISTILLATION COLUMN 248
6 ACETYLENE REACTOR 252
7 TRANSDERMAL APPLICATION OF DRUGS 257
8 GROUNDWATER FLOW 263
9 COOLING A HOT STRIP MILL 266
10 DRYING MALTODEXTRIN IN A CONVECTION OVEN 269
11 FLUID DYNAMICS OF HYDRO SYSTEMS 273
12 HOERN RADIATORS FOR SATELLITE COMMUNICATION 278
IMAGE 5
X
NUMERICAL DATA FITTING IN DYNAMICAL SYSTEMS
APPENDIX A: SOFTWARE INSTALLATION 285
1 HARDWARE AND SOFTWARE REQUIREMENTS 285
2 SYSTEM SETUP 285
3 PACKING LIST 286
APPENDIX B: TEST EXAMPLES 287
1 EXPLICIT MODEL FUNCTIONS 288
2 LAPLACE TRANSFORMS 295
3 STEADY STATE EQUATIONS 296
4 ORDINARY DIFFERENTIAL EQUATIONS 299
5 DIFFERENTIAL ALGEBRAIC EQUATIONS 317
6 PARTIAL DIFFERENTIAL EQUATIONS 320
7 PARTIAL DIFFERENTIAL ALGEBRAIC EQUATIONS 331
APPENDIX C: THE PCOMP LANGUAGE 335
APPENDIX D: GENERATION OF FORTRAN CODE 345
1 MODEL EQUATIONS 345
1.1 INPUT OF EXPLICIT MODEL FUNCTIONS 345
1.2 INPUT OF LAPLACE TRANSFORMATIONS 346
1.3 INPUT OF SYSTEMS OF STEADY STATE EQUATIONS 347
1.4 INPUT OF ORDINARY DIFFERENTIAL EQUATIONS 348
1.5 INPUT OF DIFFERENTIAL ALGEBRAIC EQUATIONS 349
1.6 INPUT OF TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS 350
1.7 INPUT OF PARTIAL DIFFERENTIAL ALGEBRAIC EQUATIONS 352
2 EXECUTION OF GENERATED CODE 355
REFERENCES 359
INDEX 387
|
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| spelling | Schittkowski, Klaus 1946- Verfasser (DE-588)133701077 aut Numerical data fitting in dynamical systems a practical introduction with applications and software Klaus Schittkowski Easy fit Dordrecht Kluwer Academic Publishers 2002 XII, 392 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Applied optimization 77 Includes bibliographical references and index. - CD-ROM u.d.T.: Easy fit Mathematisches Modell Differentiable dynamical systems Mathematical models Parameter estimation System design Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Methode der kleinsten Quadrate (DE-588)4038974-1 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Parameterschätzung (DE-588)4044614-1 s Methode der kleinsten Quadrate (DE-588)4038974-1 s DE-604 Applied optimization 77 (DE-604)BV010841718 77 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schittkowski, Klaus 1946- Numerical data fitting in dynamical systems a practical introduction with applications and software Applied optimization Mathematisches Modell Differentiable dynamical systems Mathematical models Parameter estimation System design Differenzierbares dynamisches System (DE-588)4137931-7 gnd Parameterschätzung (DE-588)4044614-1 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4044614-1 (DE-588)4038974-1 |
| title | Numerical data fitting in dynamical systems a practical introduction with applications and software |
| title_alt | Easy fit |
| title_auth | Numerical data fitting in dynamical systems a practical introduction with applications and software |
| title_exact_search | Numerical data fitting in dynamical systems a practical introduction with applications and software |
| title_full | Numerical data fitting in dynamical systems a practical introduction with applications and software Klaus Schittkowski |
| title_fullStr | Numerical data fitting in dynamical systems a practical introduction with applications and software Klaus Schittkowski |
| title_full_unstemmed | Numerical data fitting in dynamical systems a practical introduction with applications and software Klaus Schittkowski |
| title_short | Numerical data fitting in dynamical systems |
| title_sort | numerical data fitting in dynamical systems a practical introduction with applications and software |
| title_sub | a practical introduction with applications and software |
| topic | Mathematisches Modell Differentiable dynamical systems Mathematical models Parameter estimation System design Differenzierbares dynamisches System (DE-588)4137931-7 gnd Parameterschätzung (DE-588)4044614-1 gnd Methode der kleinsten Quadrate (DE-588)4038974-1 gnd |
| topic_facet | Mathematisches Modell Differentiable dynamical systems Mathematical models Parameter estimation System design Differenzierbares dynamisches System Parameterschätzung Methode der kleinsten Quadrate |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079916&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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