Parameter estimation and inverse problems:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier Academic Press
2005
|
| Schriftenreihe: | International geophysics series
90 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 301 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0120656043 |
Internformat
MARC
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| 100 | 1 | |a Aster, Richard C. |d 1960- |e Verfasser |0 (DE-588)1104397250 |4 aut | |
| 245 | 1 | 0 | |a Parameter estimation and inverse problems |c Richard C. Aster, Brian Borchers, and Clifford H. Thurber |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier Academic Press |c 2005 | |
| 300 | |a XII, 301 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International geophysics series |v 90 | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Parameter estimation | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Inversion (Geophysics) | |
| 650 | 4 | |a Mathematical models | |
| 650 | 0 | 7 | |a Inverse Methode |0 (DE-588)4162226-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geophysik |0 (DE-588)4020252-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inversion |g Geologie |0 (DE-588)4393651-9 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Thurber, Clifford H. |e Verfasser |0 (DE-588)1104401495 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804135369942237184 |
|---|---|
| adam_text | Contents
Preface
xi
1
INTRODUCTION
1
1.1
Classification
of
Inverse
Problems I
1.2
Examples of Parameter Estimation Problems
4
1.3
Examples of Inverse Problems
7
1.4
Why Inverse Problems Are Hard
11
1.5
Exercises
14
1.6
Notes and Further Reading
14
2
LINEAR REGRESSION
15
2.1
Introduction to Linear Regression
15
2.2
Statistical Aspects of Least Squares
17
2.3
Unknown Measurement Standard Deviations
26
2.4
L Regression
30
2.5
Monte Carlo Error Propagation
35
2.6
Exercises
36
2.7
Notes and Further Reading
40
3
DISCRETIZING CONTINUOUS INVERSE
PROBLEMS
41
3.1
Integral Equations
41
3.2
Quadrature Methods
41
Contents
3.3 Expansion in
Terms of
Représentera
46
3.4
Expansion
in Terms of
Orthonormal
Basis Functions
47
3.5
The Method of Backus and Gilbert
48
3.6
Exercises
52
3.7
Notes and Further Reading
54
4
RANK DEHCffiNCY AND ILL-CONDITIONING
55
4.1
The
SVD
and the Generalized Inverse
55
4.2
Covariance and Resolution of the Generalized Inverse Solution
62
4.3
Instability of the Generalized Inverse Solution
64
4.4
An Example of a Rank-Deficient Problem
67
4.5
Discrete Ill-Posed Problems
73
4.6
Exercises
85
4.7
Notes and Further Reading
87
5
TIKHONOV
REGULARIZARON
89
5.1
Selecting a Good Solution
89
5.2
SVD
Implementation of Tikhonov Regularization
91
5.3
Resolution, Bias, and Uncertainty in the Tikhonov Solution
95
5.4
Higher-Order Tikhonov Regularization
98
5.5
Resolution in Higher-Order Tikhonov Regularization
103
5.6
The TGSVD Method
105
5.7
Generalized Cross Validation
106
5.8
Error Bounds
109
5.9
Exercises
114
5.10
Notes and Further Reading
117
6
ITERATIVE METHODS
119
6.1
Introduction
119
6.2
Iterative Methods for Tomography Problems
120
6.3
The Conjugate Gradient Method
126
6.4
The CGLS Method
131
Contents
vi
6.5
Exercises
135
6.6
Notes
and Further Reading
136
7
ADDITIONALREGULAIUZATIONTECHNIQUES
139
7.1
Using Bounds as Constraints
139
7.2
Maximum Entropy Regularization
143
7.3
Total Variation
146
7.4
Exercises
151
7.5
Notes and Further Reading
152
8
FOURIER TECHNIQUES
153
8.1
Linear Systems in the Time and Frequency Domains
153
8.2
Deconvolution from a Fourier Perspective
158
8.3
Linear Systems in Discrete Time
161
8.4
Water Level Regularization
164
8.5
Exercises
168
8.6
Notes and Further Reading
170
9
NONLINEAR REGRESSION
171
9.1
Newton s Method
171
9.2
The Gauss-Newton and Levenberg-Marquardt Methods
174
9.3
Statistical Aspects
177
9.4
Implementation Issues
181
9.5
Exercises
186
9.6
Notes and Further Reading
189
10
NONLINEAR INVERSE PROBLEMS
191
10.1
Regularizing Nonlinear Least Squares Problems
191
10.2
Occam s Inversion
195
10.3
Exercises
199
10.4
Notes and Further Reading
199
Contents
11
BAYESIAN
METHODS
201
11.1
Review of the Classical Approach
201
11.2
The Bayesian Approach
202
11.3
The Multivariate Normal Case
207
11.4
Maximum Entropy Methods
212
11.5
Epilogue
214
11.6
Exercises
216
11.7
Notes and Further Reading
217
A REVIEW OF LINEAR ALGEBRA
219
A.
1
Systems of Linear Equations
219
A.2 Matrix and Vector Algebra
222
A.3 Linear Independence
228
A.4 Subspaces of R
229
A.5 Orthogonality and the Dot Product
233
A.6 Eigenvalues and Eigenvectors
237
A.7 Vector and Matrix Norms
240
A.8 The Condition Number of a Linear System
242
A.9 The QR Factorization
244
A.
10
Linear Algebra in Spaces of Functions
245
A.
11
Exercises
247
A.
12
Notes and Further Reading
249
В
REVIEW OF PROBABILITY AND STATISTICS
251
B.
1
Probability and Random Variables
251
B.2 Expected Value and Variance
257
B.3 Joint Distributions
258
B.4 Conditional Probability
262
B.5 The Multivariate Normal Distribution
264
B.6 The Central Limit Theorem
265
B.7 Testing for Normality
265
Contents ix
В.
8
Estimating Means and
Confidence
Intervals
267
B.9 Hypothesis Tests
269
B.10 Exercises
271
B
. 11
Notes and Further Reading
272
С
REVffiW OF VECTOR CALCULUS
273
C.
1
The Gradient, Hessian, and Jacobian
273
C.2 Taylor s Theorem
275
C.3
Lagrange
Multipliers
276
C.4 Exercises
278
C.5 Notes and Further Reading
280
D
GLOSSARY OF NOTATION
281
Bibliography
283
index
291
|
| adam_txt |
Contents
Preface
xi
1
INTRODUCTION
1
1.1
Classification
of
Inverse
Problems I
1.2
Examples of Parameter Estimation Problems
4
1.3
Examples of Inverse Problems
7
1.4
Why Inverse Problems Are Hard
11
1.5
Exercises
14
1.6
Notes and Further Reading
14
2
LINEAR REGRESSION
15
2.1
Introduction to Linear Regression
15
2.2
Statistical Aspects of Least Squares
17
2.3
Unknown Measurement Standard Deviations
26
2.4
L\ Regression
30
2.5
Monte Carlo Error Propagation
35
2.6
Exercises
36
2.7
Notes and Further Reading
40
3
DISCRETIZING CONTINUOUS INVERSE
PROBLEMS
41
3.1
Integral Equations
41
3.2
Quadrature Methods
41
Contents
3.3 Expansion in
Terms of
Représentera
46
3.4
Expansion
in Terms of
Orthonormal
Basis Functions
47
3.5
The Method of Backus and Gilbert
48
3.6
Exercises
52
3.7
Notes and Further Reading
54
4
RANK DEHCffiNCY AND ILL-CONDITIONING
55
4.1
The
SVD
and the Generalized Inverse
55
4.2
Covariance and Resolution of the Generalized Inverse Solution
62
4.3
Instability of the Generalized Inverse Solution
64
4.4
An Example of a Rank-Deficient Problem
67
4.5
Discrete Ill-Posed Problems
73
4.6
Exercises
85
4.7
Notes and Further Reading
87
5
TIKHONOV
REGULARIZARON
89
5.1
Selecting a Good Solution
89
5.2
SVD
Implementation of Tikhonov Regularization
91
5.3
Resolution, Bias, and Uncertainty in the Tikhonov Solution
95
5.4
Higher-Order Tikhonov Regularization
98
5.5
Resolution in Higher-Order Tikhonov Regularization
103
5.6
The TGSVD Method
105
5.7
Generalized Cross Validation
106
5.8
Error Bounds
109
5.9
Exercises
114
5.10
Notes and Further Reading
117
6
ITERATIVE METHODS
119
6.1
Introduction
119
6.2
Iterative Methods for Tomography Problems
120
6.3
The Conjugate Gradient Method
126
6.4
The CGLS Method
131
Contents
vi
6.5
Exercises
135
6.6
Notes
and Further Reading
136
7
ADDITIONALREGULAIUZATIONTECHNIQUES
139
7.1
Using Bounds as Constraints
139
7.2
Maximum Entropy Regularization
143
7.3
Total Variation
146
7.4
Exercises
151
7.5
Notes and Further Reading
152
8
FOURIER TECHNIQUES
153
8.1
Linear Systems in the Time and Frequency Domains
153
8.2
Deconvolution from a Fourier Perspective
158
8.3
Linear Systems in Discrete Time
161
8.4
Water Level Regularization
164
8.5
Exercises
168
8.6
Notes and Further Reading
170
9
NONLINEAR REGRESSION
171
9.1
Newton's Method
171
9.2
The Gauss-Newton and Levenberg-Marquardt Methods
174
9.3
Statistical Aspects
177
9.4
Implementation Issues
181
9.5
Exercises
186
9.6
Notes and Further Reading
189
10
NONLINEAR INVERSE PROBLEMS
191
10.1
Regularizing Nonlinear Least Squares Problems
191
10.2
Occam's Inversion
195
10.3
Exercises
199
10.4
Notes and Further Reading
199
Contents
11
BAYESIAN
METHODS
201
11.1
Review of the Classical Approach
201
11.2
The Bayesian Approach
202
11.3
The Multivariate Normal Case
207
11.4
Maximum Entropy Methods
212
11.5
Epilogue
214
11.6
Exercises
216
11.7
Notes and Further Reading
217
A REVIEW OF LINEAR ALGEBRA
219
A.
1
Systems of Linear Equations
219
A.2 Matrix and Vector Algebra
222
A.3 Linear Independence
228
A.4 Subspaces of R"
229
A.5 Orthogonality and the Dot Product
233
A.6 Eigenvalues and Eigenvectors
237
A.7 Vector and Matrix Norms
240
A.8 The Condition Number of a Linear System
242
A.9 The QR Factorization
244
A.
10
Linear Algebra in Spaces of Functions
245
A.
11
Exercises
247
A.
12
Notes and Further Reading
249
В
REVIEW OF PROBABILITY AND STATISTICS
251
B.
1
Probability and Random Variables
251
B.2 Expected Value and Variance
257
B.3 Joint Distributions
258
B.4 Conditional Probability
262
B.5 The Multivariate Normal Distribution
264
B.6 The Central Limit Theorem
265
B.7 Testing for Normality
265
Contents ix
В.
8
Estimating Means and
Confidence
Intervals
267
B.9 Hypothesis Tests
269
B.10 Exercises
271
B
. 11
Notes and Further Reading
272
С
REVffiW OF VECTOR CALCULUS
273
C.
1
The Gradient, Hessian, and Jacobian
273
C.2 Taylor's Theorem
275
C.3
Lagrange
Multipliers
276
C.4 Exercises
278
C.5 Notes and Further Reading
280
D
GLOSSARY OF NOTATION
281
Bibliography
283
index
291 |
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| id | DE-604.BV021592505 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:44:58Z |
| indexdate | 2024-07-09T20:39:25Z |
| institution | BVB |
| isbn | 0120656043 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014807959 |
| oclc_num | 57470064 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-83 DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-83 DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XII, 301 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Elsevier Academic Press |
| record_format | marc |
| series | International geophysics series |
| series2 | International geophysics series |
| spelling | Aster, Richard C. 1960- Verfasser (DE-588)1104397250 aut Parameter estimation and inverse problems Richard C. Aster, Brian Borchers, and Clifford H. Thurber Amsterdam [u.a.] Elsevier Academic Press 2005 XII, 301 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier International geophysics series 90 Mathematisches Modell Parameter estimation Inverse problems (Differential equations) Inversion (Geophysics) Mathematical models Inverse Methode (DE-588)4162226-1 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Geophysik (DE-588)4020252-5 gnd rswk-swf Inversion Geologie (DE-588)4393651-9 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Geophysik (DE-588)4020252-5 s Inverse Methode (DE-588)4162226-1 s DE-604 Parameterschätzung (DE-588)4044614-1 s Inverses Problem (DE-588)4125161-1 s Inversion Geologie (DE-588)4393651-9 s 1\p DE-604 Thurber, Clifford H. Verfasser (DE-588)1104401495 aut Borchers, Brian Verfasser (DE-588)1104398079 aut International geophysics series 90 (DE-604)BV000005107 90 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014807959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aster, Richard C. 1960- Thurber, Clifford H. Borchers, Brian Parameter estimation and inverse problems International geophysics series Mathematisches Modell Parameter estimation Inverse problems (Differential equations) Inversion (Geophysics) Mathematical models Inverse Methode (DE-588)4162226-1 gnd Inverses Problem (DE-588)4125161-1 gnd Geophysik (DE-588)4020252-5 gnd Inversion Geologie (DE-588)4393651-9 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4162226-1 (DE-588)4125161-1 (DE-588)4020252-5 (DE-588)4393651-9 (DE-588)4044614-1 |
| title | Parameter estimation and inverse problems |
| title_auth | Parameter estimation and inverse problems |
| title_exact_search | Parameter estimation and inverse problems |
| title_exact_search_txtP | Parameter estimation and inverse problems |
| title_full | Parameter estimation and inverse problems Richard C. Aster, Brian Borchers, and Clifford H. Thurber |
| title_fullStr | Parameter estimation and inverse problems Richard C. Aster, Brian Borchers, and Clifford H. Thurber |
| title_full_unstemmed | Parameter estimation and inverse problems Richard C. Aster, Brian Borchers, and Clifford H. Thurber |
| title_short | Parameter estimation and inverse problems |
| title_sort | parameter estimation and inverse problems |
| topic | Mathematisches Modell Parameter estimation Inverse problems (Differential equations) Inversion (Geophysics) Mathematical models Inverse Methode (DE-588)4162226-1 gnd Inverses Problem (DE-588)4125161-1 gnd Geophysik (DE-588)4020252-5 gnd Inversion Geologie (DE-588)4393651-9 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Mathematisches Modell Parameter estimation Inverse problems (Differential equations) Inversion (Geophysics) Mathematical models Inverse Methode Inverses Problem Geophysik Inversion Geologie Parameterschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014807959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005107 |
| work_keys_str_mv | AT asterrichardc parameterestimationandinverseproblems AT thurbercliffordh parameterestimationandinverseproblems AT borchersbrian parameterestimationandinverseproblems |