Regularization for applied inverse and ill-posed problems: a numerical approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Leipzig
Teubner
1986
|
| Edition: | 1. Aufl. |
| Series: | Teubner-Texte zur Mathematik
85 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 196 S. |
| ISBN: | 3322003418 9783322930354 |
Staff View
MARC
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| 100 | 1 | |a Hofmann, Bernd |d 1953- |e Verfasser |0 (DE-588)129638684 |4 aut | |
| 245 | 1 | 0 | |a Regularization for applied inverse and ill-posed problems |b a numerical approach |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Leipzig |b Teubner |c 1986 | |
| 300 | |a 196 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 85 | |
| 650 | 4 | |a Analyse numérique | |
| 650 | 4 | |a Problèmes inversés (Équations différentielles) - Solutions numériques | |
| 650 | 4 | |a Inverse problems (Differential equations) |x Numerical solutions | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regularisierung |0 (DE-588)4124043-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | 1 | |a Regularisierung |0 (DE-588)4124043-1 |D s |
| 689 | 0 | 2 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
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Record in the Search Index
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CONTENTS
1. Introduction 7
2. Mathematical Modelling 12
2.1. Formulation, Discretization and Properties'of
Inverse Problems . 12
2.2. A Survey of the Ill Posedness Phenomenon via
Examples 21
2.2.1. Linear Fredholm Integral Equations of the
* First Kind in Banach Spaces . 21
2.2.2. Linear Volterra Integral Equations of the
First Kind in Hilbert Spaces 27
2.2.3. The Linear Identification Problem of
Computerized Tomography 36
2.2.4. A Nonlinear Identification Problem of
Convolution Type . 38
2.2.5. Identification in Heat Equation Problems. . 42
2.2.6. Identification in a Coupled System of
Integral Equations of the First Kind . 50
2.2.7. On a Parabolic Boundary Control Problem
Arising in Bheology • 53
2.2.8. An Inverse Eigenvalue Problem 55
2.3. On A Priori Information 57
3. A General Optimization Approach 61
3.1. Optimal Solutions to Noisy Semi Biscretized
Problems 61
3.1.1. Identification Problems 61
3.1.2. Control Problems 72
3.2. Optimal Solutions to Noisy Discretized Problems. . 75
3.2.1. Model Assumptions 75
3.2.2. Asymptotic Properties 77
3.3. Uncertainty of Approximate Solutions 80
4. Eegularization of Deterministic Diseretized Inverse
Problems 85
4.1. Constrained Tikhonov Regularization 85
4.1.1. Regularized Solutions 85
4.1.2. Regularization as a Lagrange Multiplier
Method 91
4.1.3. Alternative Strategies for Choosing the
Regularization Parameter 95
4.2. Multi Parameter Regularization 97
4.3. Descriptive, Adaptive and Iterative Regularization 103
4.4. Regularization of Unconstrained Problems 105
4.4.1. Euler's Equation 105
4.4.2. Regularization of a System of Linear
Algebraic Equations 108
4.4.3. A Singular Value Analysis of Regularization 113
5. Regularization of Stochastic Diacretized Inverse
Problems 118
5.1. The Non Bayesian Case 118
5.1.1. Linear Estimators in the Linear Model . . . 118
5.1.2. Ridge Estimators and Cross Validation . . . 127
5.1.3. The Reduction Problem 130
5.1.4. Remarks on the Nonlinear Model 133
5
5.2. The Bayesian Case 134
5.2.1. Statistical Regularizaiiion 134
5.2.2. Empirical Statistical Regularization . 140
5.3. On an Example Concerning the Stochastic
Modelling 144
6. A Unified Numerical Approach to Nonlinear Inverse
Problems 147
6.1. Classifying Inverse Problems with Respect to the
Amount of Computation 147
6.2. A Numerical Route for Computing Regularised
Solutions 151
6.3. Some Remarks on Software 155
6.4. An Iterative Refinement 157
Notations 164
Bibliography 167
Index 195
6 |
| any_adam_object | 1 |
| author | Hofmann, Bernd 1953- |
| author_GND | (DE-588)129638684 |
| author_facet | Hofmann, Bernd 1953- |
| author_role | aut |
| author_sort | Hofmann, Bernd 1953- |
| author_variant | b h bh |
| building | Verbundindex |
| bvnumber | BV003653698 |
| callnumber-first | Q - Science |
| callnumber-label | QA371 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 SK 920 |
| ctrlnum | (OCoLC)246866465 (DE-599)BVBBV003653698 |
| 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 |
| edition | 1. Aufl. |
| format | Book |
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| id | DE-604.BV003653698 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-28T11:10:52Z |
| institution | BVB |
| isbn | 3322003418 9783322930354 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002326901 |
| oclc_num | 246866465 |
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| physical | 196 S. |
| psigel | TUB-nb |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Hofmann, Bernd 1953- Verfasser (DE-588)129638684 aut Regularization for applied inverse and ill-posed problems a numerical approach 1. Aufl. Leipzig Teubner 1986 196 S. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 85 Analyse numérique Problèmes inversés (Équations différentielles) - Solutions numériques Inverse problems (Differential equations) Numerical solutions Numerical analysis Inverses Problem (DE-588)4125161-1 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Regularisierung (DE-588)4124043-1 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Inverses Problem (DE-588)4125161-1 s Regularisierung (DE-588)4124043-1 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s DE-604 Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Teubner-Texte zur Mathematik 85 (DE-604)BV000012607 85 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002326901&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 | Hofmann, Bernd 1953- Regularization for applied inverse and ill-posed problems a numerical approach Teubner-Texte zur Mathematik Analyse numérique Problèmes inversés (Équations différentielles) - Solutions numériques Inverse problems (Differential equations) Numerical solutions Numerical analysis Inverses Problem (DE-588)4125161-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Regularisierung (DE-588)4124043-1 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| subject_GND | (DE-588)4125161-1 (DE-588)4042805-9 (DE-588)4124043-1 (DE-588)4186951-5 |
| title | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_auth | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_exact_search | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_full | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_fullStr | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_full_unstemmed | Regularization for applied inverse and ill-posed problems a numerical approach |
| title_short | Regularization for applied inverse and ill-posed problems |
| title_sort | regularization for applied inverse and ill posed problems a numerical approach |
| title_sub | a numerical approach |
| topic | Analyse numérique Problèmes inversés (Équations différentielles) - Solutions numériques Inverse problems (Differential equations) Numerical solutions Numerical analysis Inverses Problem (DE-588)4125161-1 gnd Numerische Mathematik (DE-588)4042805-9 gnd Regularisierung (DE-588)4124043-1 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| topic_facet | Analyse numérique Problèmes inversés (Équations différentielles) - Solutions numériques Inverse problems (Differential equations) Numerical solutions Numerical analysis Inverses Problem Numerische Mathematik Regularisierung Inkorrekt gestelltes Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002326901&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT hofmannbernd regularizationforappliedinverseandillposedproblemsanumericalapproach |