Stable solution of inverse problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Braunschweig u.a.
Vieweg
1987
|
| Schriftenreihe: | Advanced lectures in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 254 S. |
| ISBN: | 352808961X |
Internformat
MARC
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| 100 | 1 | |a Baumeister, Johann |d 1944- |e Verfasser |0 (DE-588)144033399 |4 aut | |
| 245 | 1 | 0 | |a Stable solution of inverse problems |
| 264 | 1 | |a Braunschweig u.a. |b Vieweg |c 1987 | |
| 300 | |a VIII, 254 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Advanced lectures in mathematics | |
| 650 | 4 | |a Problème inverse | |
| 650 | 7 | |a Problèmes inverses (équations différentielles) - Solutions numériques |2 ram | |
| 650 | 7 | |a Problèmes inverses (équations différentielles) |2 ram | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Inverse problems (Differential equations) |x Numerical solutions | |
| 650 | 0 | 7 | |a Stabile Lösung |0 (DE-588)4138702-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | VI
TABLE OF CONTENTS
PART I BASIC CONCEPTS
Chapter 1 Introduction 1
1.1 Inverse problems 1
1.2 Some examples of inverse problems 4
1.3 Analysis of inverse problems 14
Chapter 2 Ill posed problems 16
2.1 General properties 16
2.2 Restoration of continuity in the linear case 18
2.3 Stability estimates 23
Chapter 3 Regularization 27
3.1 Reconstruction from non exact data 27
3.2 Preliminary results on Tikhonov s method 34
3.3 Regularizing schemes 37
3.4 A tutorial example: The reconstruction of a
derivative 41
3.5 Optimal reconstruction of linear functionals 43
PART II REGULARIZATION METHODS
Chapter 4 The singular value decomposition 49
4.1 Compact operators 49
4.2 The spectrum of compact selfadjoint operators 53
4.3 The singular value decomposition 57
4.4 The min max principle 64
4.5 The asymptotics of singular values 66
4.6 Picard s criterion 70
Chapter 5 Applications of the singular value
decomposition 73
5.1 Hilbert scales 73
5.2 Convergence of regularizing schemes 78
5.3 On the use of the conjugate gradient method 82
5.4 n widths 88
VII
Chapter 6 The method of Tikhonov 91
6.1 The generalized inverse 91
6.2 The classical method of Tikhonov 97
6.3 Error bounds for Tikhonov regularization
in Hilbert scales 99
6.4 On discrepancy principles 102
6.5 Discretization in Tikhonov1s method 109
Chapter 7 Regularization by discretization 112
7.1 Discretization by projection methods 112
7.2 Quasioptimality and robustness 116
7.3 Specific methods 120
7.4 Asymptotic estimates 123
PART III LEAST SQUARES SOLUTIONS OF SYSTEMS OF
LINEAR EQUATIONS
Chapter 8 Least squares problems 127
8.1 The singular value decomposition of a matrix 127
8.2 The pseudo inverse 133
8.3 Least squares solutions 138
8.4 Perturbation results 141
8.5 Application: Fitting of data 149
Chapter 9 Numerical aspects of least squares problems 152
9.1 Calculation of A : The factorization approach 152
9.2 Rank decision 158
9.3 Cross validation 161
9.4 Successive approximation 164
9.5 The ART algorithm 171
PART IV SPECIFIC TOPICS
Chapter 10 Convolution equations 179
10.1 The Fourier transform 179
10.2 Regularization of convolution equations 183
10.3 On the discretization of convolution
equations 190
10.4 Reconstruction by successive approximation 195
VIII
Chapter 11 The final value problem 203
11.1 Introduction 203
11.2 The mild solution of the forward problem 207
11.3 The Hilbert scales E . 211
a, t
11.4 Regularizing schemes 214
Chapter 12 Parameter identification 221
12.1 Identifiability of parameters in dynamical
systems 221
12.2 Identification in linear dynamic systems 224
12.3 Identification in bilinear structures 228
12.4 Adaptive identification 237
REFERENCES 245
NOTATIONS 251
SUBJECT INDEX 252
|
| any_adam_object | 1 |
| author | Baumeister, Johann 1944- |
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| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Inverse Problems gnd |
| genre_facet | Inverse Problems |
| id | DE-604.BV000669331 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:31Z |
| institution | BVB |
| isbn | 352808961X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000417680 |
| oclc_num | 16156812 |
| open_access_boolean | |
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| physical | VIII, 254 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Vieweg |
| record_format | marc |
| series2 | Advanced lectures in mathematics |
| spelling | Baumeister, Johann 1944- Verfasser (DE-588)144033399 aut Stable solution of inverse problems Braunschweig u.a. Vieweg 1987 VIII, 254 S. txt rdacontent n rdamedia nc rdacarrier Advanced lectures in mathematics Problème inverse Problèmes inverses (équations différentielles) - Solutions numériques ram Problèmes inverses (équations différentielles) ram Inverse problems (Differential equations) Inverse problems (Differential equations) Numerical solutions Stabile Lösung (DE-588)4138702-8 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Inverse Problems gnd rswk-swf Inverse Problems f Stabile Lösung (DE-588)4138702-8 s DE-604 Inverses Problem (DE-588)4125161-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baumeister, Johann 1944- Stable solution of inverse problems Problème inverse Problèmes inverses (équations différentielles) - Solutions numériques ram Problèmes inverses (équations différentielles) ram Inverse problems (Differential equations) Inverse problems (Differential equations) Numerical solutions Stabile Lösung (DE-588)4138702-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4138702-8 (DE-588)4125161-1 |
| title | Stable solution of inverse problems |
| title_auth | Stable solution of inverse problems |
| title_exact_search | Stable solution of inverse problems |
| title_full | Stable solution of inverse problems |
| title_fullStr | Stable solution of inverse problems |
| title_full_unstemmed | Stable solution of inverse problems |
| title_short | Stable solution of inverse problems |
| title_sort | stable solution of inverse problems |
| topic | Problème inverse Problèmes inverses (équations différentielles) - Solutions numériques ram Problèmes inverses (équations différentielles) ram Inverse problems (Differential equations) Inverse problems (Differential equations) Numerical solutions Stabile Lösung (DE-588)4138702-8 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Problème inverse Problèmes inverses (équations différentielles) - Solutions numériques Problèmes inverses (équations différentielles) Inverse problems (Differential equations) Inverse problems (Differential equations) Numerical solutions Stabile Lösung Inverses Problem Inverse Problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417680&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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