Aspects of regularization in Banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2010
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 138 S. graph. Darst. 21 cm |
| ISBN: | 9783832527310 |
Staff View
MARC
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| 100 | 1 | |a Kazimierski, Kamil S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Aspects of regularization in Banach spaces |c Kamil S. Kazimierski |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2010 | |
| 300 | |a 138 S. |b graph. Darst. |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Bremen, Univ., Diss., 2010 | ||
| 650 | 7 | |a Banach-Raum |2 swd | |
| 650 | 7 | |a Linearer Operator |2 swd | |
| 650 | 7 | |a Inverses Problem |2 swd | |
| 650 | 7 | |a Regularisierung |2 swd | |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regularisierung |0 (DE-588)4124043-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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| 689 | 0 | 1 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | 2 | |a Regularisierung |0 (DE-588)4124043-1 |D s |
| 689 | 0 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-022634854 | ||
Record in the Search Index
| _version_ | 1804145794995978240 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 EXAMPLE: VELOCITY RETRIEVAL FROM GPS DATA 3
2 PRELIMINARIES AND BASIC DEFINITIONS 7
2.1 GENERAL 7
2.2 CONVEX ANALYSIS 9
2.2.1 DUALITY MAPPING 13
2.3 GEOMETRY OF BANACH SPACE NORMS 15
2.3.1 CONVEXITY AND SMOOTHNESS OF POWER TYPE 16
2.3.2 BREGMAN DISTANCES 21
2.4 REGULARIZATION THEORY 26
3 GEOMETRY OF BESOV SPACES 27
3.1 SOBOLEV SPACES 28
3.2 (SEQUENCE) BESOV SPACES 29
3.3 CONVEXITY AND SMOOTHNESS OF P SPACES 34
3.4 SPACES^ 34
3.5 SPACES * 36
3.6 CONVEXITY AND SMOOTHNESS OF E%F 37
3.7 CONSEQUENCES TO SEQUENCE BESOV SPACES 40
4 TIKHONOV REGULARIZATION 43
4.1 REGULARIZATION PROPERTIES OF TIKHONOV FUNCTIONALS 46
4.2 SOURCE CONDITIONS 47
4.2.1 LOW ORDER SOURCE CONDITION 47
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009698222
DIGITALISIERT DURCH
IMAGE 2
4.2.2 HIGH ORDER SOURCE CONDITION 48
4.3 CHOICE OF THE REGULARIZATION PARAMETER 51
4.3.1 A-PRIORI PARAMETER CHOICE 52
4.3.2 MOROZOV S DISCREPANCY PRINCIPLE 54
4.3.3 ENGL S DISCREPANCY PRINCIPLE 55
4.4 MINIMIZATION OF THE TIKHONOV FUNCTIONAL 61
4.4.1 UPDATE IN THE PRIMAL SPACE 63
4.4.2 UPDATE IN THE DUAL SPACE 69
LANDWEBER REGULARIZATION 77
5.1 LANDWEBER REGULARIZATION 79
5.2 MODIFIED LANDWEBER REGULARIZATION 84
NUMERICAL EXPERIMENTS 89
6.1 UPDATE IN THE PRIMAL SPACE 89
6.2 UPDATE IN THE DUAL SPACE 93
6.3 ENGL S DISCREPANCY PRINCIPLE 113
6.4 (MODIFIED) LANDWEBER ITERATION 121
FINAL REMARKS 125
PROOF OF REGULARIZATION PROPERTIES OF TIKHONOV FUNCTIONAL 129
|
| any_adam_object | 1 |
| author | Kazimierski, Kamil S. |
| author_facet | Kazimierski, Kamil S. |
| author_role | aut |
| author_sort | Kazimierski, Kamil S. |
| author_variant | k s k ks ksk |
| building | Verbundindex |
| bvnumber | BV037483330 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)724309156 (DE-599)BVBBV037483330 |
| dewey-full | 515.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.732 |
| dewey-search | 515.732 |
| dewey-sort | 3515.732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV037483330 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:25:07Z |
| institution | BVB |
| isbn | 9783832527310 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022634854 |
| oclc_num | 724309156 |
| open_access_boolean | |
| owner | DE-634 DE-384 |
| owner_facet | DE-634 DE-384 |
| physical | 138 S. graph. Darst. 21 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Kazimierski, Kamil S. Verfasser aut Aspects of regularization in Banach spaces Kamil S. Kazimierski Berlin Logos-Verl. 2010 138 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Bremen, Univ., Diss., 2010 Banach-Raum swd Linearer Operator swd Inverses Problem swd Regularisierung swd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Regularisierung (DE-588)4124043-1 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Banach-Raum (DE-588)4004402-6 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s Regularisierung (DE-588)4124043-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022634854&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kazimierski, Kamil S. Aspects of regularization in Banach spaces Banach-Raum swd Linearer Operator swd Inverses Problem swd Regularisierung swd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Regularisierung (DE-588)4124043-1 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4186951-5 (DE-588)4124043-1 (DE-588)4004402-6 (DE-588)4113937-9 |
| title | Aspects of regularization in Banach spaces |
| title_auth | Aspects of regularization in Banach spaces |
| title_exact_search | Aspects of regularization in Banach spaces |
| title_full | Aspects of regularization in Banach spaces Kamil S. Kazimierski |
| title_fullStr | Aspects of regularization in Banach spaces Kamil S. Kazimierski |
| title_full_unstemmed | Aspects of regularization in Banach spaces Kamil S. Kazimierski |
| title_short | Aspects of regularization in Banach spaces |
| title_sort | aspects of regularization in banach spaces |
| topic | Banach-Raum swd Linearer Operator swd Inverses Problem swd Regularisierung swd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd Regularisierung (DE-588)4124043-1 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Banach-Raum Linearer Operator Inverses Problem Regularisierung Inkorrekt gestelltes Problem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022634854&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kazimierskikamils aspectsofregularizationinbanachspaces |