Iterative regularization methods for nonlinear ill-posed problems:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2008
|
| Schriftenreihe: | Radon series on computational and applied mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 194 S. graph. Darst. |
| ISBN: | 9783110204209 |
Internformat
MARC
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| 100 | 1 | |a Kaltenbacher, Barbara |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Iterative regularization methods for nonlinear ill-posed problems |c Barbara Kaltenbacher ; Andreas Neubauer ; Otmar Scherzer |
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2008 | |
| 300 | |a VIII, 194 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Radon series on computational and applied mathematics |v 6 | |
| 650 | 4 | |a Differential equations, Partial |x Improperly posed problems | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
| 650 | 0 | 7 | |a Iteration |0 (DE-588)4123457-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares inverses Problem |0 (DE-588)4453043-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regularisierungsverfahren |0 (DE-588)4846428-4 |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 Nichtlineares inverses Problem |0 (DE-588)4453043-2 |D s |
| 689 | 0 | 1 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | 2 | |a Regularisierungsverfahren |0 (DE-588)4846428-4 |D s |
| 689 | 0 | 3 | |a Iteration |0 (DE-588)4123457-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Neubauer, Andreas |e Verfasser |4 aut | |
| 700 | 1 | |a Scherzer, Otmar |d 1964- |e Verfasser |0 (DE-588)120650053 |4 aut | |
| 830 | 0 | |a Radon series on computational and applied mathematics |v 6 |w (DE-604)BV023335470 |9 6 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016496138 | ||
Datensatz im Suchindex
| _version_ | 1804137646114471936 |
|---|---|
| adam_text | Contents
Preface
....................................
v
1
Introduction
............................... 1
1.1
Régularisation
methods
....................... 2
1.2
Iterative regularization methods
.................. 3
2
Nonlinear
Landweber
iteration
.................... 5
2.1
Basic conditions
........................... 5
2.2
Convergence of the
Landweber
iteration
.............. 8
2.3
Convergence rates
.......................... 13
2.4
An example
............................. 26
3
Modified
Landweber
methods
..................... 30
3.1 Landweber
iteration in Hubert scales
................ 30
3.2
Iteratively regularized
Landweber
iteration
............. 41
3.3
A derivative free approach
..................... 52
3.4
Steepest descent and minimal error method
............ 54
3.5
The Landweber-Kaczmarz method
................. 58
4
Newton type methods
.......................... 64
4.1
Levenberg-Marquardt method
................... 64
4.2
Iteratively regularized Gauss-Newton method
........... 77
4.3
Generalizations of the iteratively regularized Gauss-Newton method
91
4.4
Broyden s method for ill-posed problems
............. 113
5
Multilevel methods
........................... 134
5.1
Regularization by discretization
.................. 134
5.2
Multigrid methods
......................... 138
6
Level set methods
............................ 150
6.1
Continuous regularization
...................... 152
6.2
Level set regularization
....................... 161
7
Applications
............................... 170
7.1
Reconstruction of transducer pressure fields from
Schlieren
images
170
7.2
Identification of
B
-Н
curves in nonlinear magnetics
........ 173
viii Contents
8
Comments
................................181
Bibliography
.................................183
Index
.....................................193
|
| adam_txt |
Contents
Preface
.
v
1
Introduction
. 1
1.1
Régularisation
methods
. 2
1.2
Iterative regularization methods
. 3
2
Nonlinear
Landweber
iteration
. 5
2.1
Basic conditions
. 5
2.2
Convergence of the
Landweber
iteration
. 8
2.3
Convergence rates
. 13
2.4
An example
. 26
3
Modified
Landweber
methods
. 30
3.1 Landweber
iteration in Hubert scales
. 30
3.2
Iteratively regularized
Landweber
iteration
. 41
3.3
A derivative free approach
. 52
3.4
Steepest descent and minimal error method
. 54
3.5
The Landweber-Kaczmarz method
. 58
4
Newton type methods
. 64
4.1
Levenberg-Marquardt method
. 64
4.2
Iteratively regularized Gauss-Newton method
. 77
4.3
Generalizations of the iteratively regularized Gauss-Newton method
91
4.4
Broyden's method for ill-posed problems
. 113
5
Multilevel methods
. 134
5.1
Regularization by discretization
. 134
5.2
Multigrid methods
. 138
6
Level set methods
. 150
6.1
Continuous regularization
. 152
6.2
Level set regularization
. 161
7
Applications
. 170
7.1
Reconstruction of transducer pressure fields from
Schlieren
images
170
7.2
Identification of
B
-Н
curves in nonlinear magnetics
. 173
viii Contents
8
Comments
.181
Bibliography
.183
Index
.193 |
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| author | Kaltenbacher, Barbara Neubauer, Andreas Scherzer, Otmar 1964- |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV023311885 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:50:35Z |
| indexdate | 2024-07-09T21:15:36Z |
| institution | BVB |
| isbn | 9783110204209 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016496138 |
| oclc_num | 232124307 |
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| physical | VIII, 194 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | De Gruyter |
| record_format | marc |
| series | Radon series on computational and applied mathematics |
| series2 | Radon series on computational and applied mathematics |
| spelling | Kaltenbacher, Barbara Verfasser aut Iterative regularization methods for nonlinear ill-posed problems Barbara Kaltenbacher ; Andreas Neubauer ; Otmar Scherzer Berlin [u.a.] De Gruyter 2008 VIII, 194 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Radon series on computational and applied mathematics 6 Differential equations, Partial Improperly posed problems Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd rswk-swf Nichtlineares inverses Problem (DE-588)4453043-2 gnd rswk-swf Regularisierungsverfahren (DE-588)4846428-4 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Nichtlineares inverses Problem (DE-588)4453043-2 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s Regularisierungsverfahren (DE-588)4846428-4 s Iteration (DE-588)4123457-1 s DE-604 Neubauer, Andreas Verfasser aut Scherzer, Otmar 1964- Verfasser (DE-588)120650053 aut Radon series on computational and applied mathematics 6 (DE-604)BV023335470 6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016496138&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaltenbacher, Barbara Neubauer, Andreas Scherzer, Otmar 1964- Iterative regularization methods for nonlinear ill-posed problems Radon series on computational and applied mathematics Differential equations, Partial Improperly posed problems Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd Nichtlineares inverses Problem (DE-588)4453043-2 gnd Regularisierungsverfahren (DE-588)4846428-4 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4453043-2 (DE-588)4846428-4 (DE-588)4186951-5 |
| title | Iterative regularization methods for nonlinear ill-posed problems |
| title_auth | Iterative regularization methods for nonlinear ill-posed problems |
| title_exact_search | Iterative regularization methods for nonlinear ill-posed problems |
| title_exact_search_txtP | Iterative regularization methods for nonlinear ill-posed problems |
| title_full | Iterative regularization methods for nonlinear ill-posed problems Barbara Kaltenbacher ; Andreas Neubauer ; Otmar Scherzer |
| title_fullStr | Iterative regularization methods for nonlinear ill-posed problems Barbara Kaltenbacher ; Andreas Neubauer ; Otmar Scherzer |
| title_full_unstemmed | Iterative regularization methods for nonlinear ill-posed problems Barbara Kaltenbacher ; Andreas Neubauer ; Otmar Scherzer |
| title_short | Iterative regularization methods for nonlinear ill-posed problems |
| title_sort | iterative regularization methods for nonlinear ill posed problems |
| topic | Differential equations, Partial Improperly posed problems Iterative methods (Mathematics) Iteration (DE-588)4123457-1 gnd Nichtlineares inverses Problem (DE-588)4453043-2 gnd Regularisierungsverfahren (DE-588)4846428-4 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| topic_facet | Differential equations, Partial Improperly posed problems Iterative methods (Mathematics) Iteration Nichtlineares inverses Problem Regularisierungsverfahren Inkorrekt gestelltes Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016496138&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023335470 |
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