On L1-approximation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Pr.
1989
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
93 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 239 S. |
| ISBN: | 052136650X |
Internformat
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| 245 | 1 | 0 | |a On L1-approximation |c Allan M. Pinkus |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1989 | |
| 300 | |a X, 239 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 93 | |
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Datensatz im Suchindex
| _version_ | 1804116947051216896 |
|---|---|
| adam_text | Contents
Preface ix
1 Preliminaries 1
1. Existence 1
2. Characterization 2
3. Uniqueness and Strong Uniqueness 6
4. Continuity 8
Exercises 10
Notes and References 11
2 Approximation from Finite-Dimensional Subspaces of L1 13
1. Introduction and Notation 13
2. Characterization 14
3. Uniqueness 17
4. Continuous Selections 25
Exercises 27
Notes and References 29
3 Approximation from Finite-Dimensional Subspaces in Ci(K,fi) 30
1. Introduction and Notation 30
2. Uniqueness 31
3. Best Approximation with Constraints: An Example 39
4. fc-Convexity 42
5. Continuous Selections 44
Exercises 54
Notes and References 55
4 Unicity Subspaces and Property A 57
1. Introduction 57
2. Property A 58
3. Consequences of Property A 63
4. Characterizing Property A on M 74
5. Property A on JRd, d 2 86
6. Best Approximation under Interpolation: An Example 91
7. Property A* and fc-Convexity 92
Exercises 97
Notes and References 98
viii Contents
5 One-Sided L1-Approximation 101
1. Introduction 101
2. Best One-Sided Approximation in C(K): Characterization 102
3. Best One-Sided Approximation in C(K): Uniqueness 107
4. Unicity Spaces for all fi 113
5. Best One-Sided Approximation in ^(K) 115
6. Property B 121
Exercises 129
Notes and References 130
6 Discrete ^ -Approximation 132
1. Introduction 132
2. Two-Sided ^-Approximation 132
3. One-Sided ^ -Approximation 147
Exercises 150
Notes and References 152
7 Algorithms 153
1. Introduction 153
2. Gradients and Subgradients 153
3. One-Sided (.?-Approximation 159
4. Two-Sided ^ -Approximation 161
5. One-Sided L1-Approximation 170
6. Two-Sided L1-Approximation 181
Notes and References 192
Appendix A. T- and WT-Systems 194
Part I. T-Systems 194
Part II. NT-Systems 198
Appendix B. Convexity Cones and L1-Approximation 207
Part I. Two-Sided L1-Approximation 207
Part II. One-Sided /^-Approximation 214
References 228
Author Index 236
Subject Index 238
|
| any_adam_object | 1 |
| author | Pinkus, Allan 1946- |
| author_GND | (DE-588)110369297 |
| author_facet | Pinkus, Allan 1946- |
| author_role | aut |
| author_sort | Pinkus, Allan 1946- |
| author_variant | a p ap |
| building | Verbundindex |
| bvnumber | BV002545963 |
| callnumber-first | Q - Science |
| callnumber-label | QA221 |
| callnumber-raw | QA221 |
| callnumber-search | QA221 |
| callnumber-sort | QA 3221 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 470 |
| classification_tum | MAT 417f |
| ctrlnum | (OCoLC)19066359 (DE-599)BVBBV002545963 |
| dewey-full | 511/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.4 |
| dewey-search | 511/.4 |
| dewey-sort | 3511 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV002545963 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:46:36Z |
| institution | BVB |
| isbn | 052136650X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001638755 |
| oclc_num | 19066359 |
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| physical | X, 239 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Pinkus, Allan 1946- Verfasser (DE-588)110369297 aut On L1-approximation Allan M. Pinkus 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1989 X, 239 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 93 Approximation, Théorie de l' ram théorie approximation inriac Approximation theory Least absolute deviations (Statistics) Beste Approximation (DE-588)4144932-0 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Kleinste absolute Abweichung (DE-588)4501130-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf L1-Approximation (DE-588)4449479-8 gnd rswk-swf Čebyšev-Raum (DE-588)4147436-3 gnd rswk-swf Kleinste absolute Abweichung (DE-588)4501130-8 s Approximationstheorie (DE-588)4120913-8 s DE-604 L1-Approximation (DE-588)4449479-8 s Beste Approximation (DE-588)4144932-0 s Čebyšev-Raum (DE-588)4147436-3 s Approximation (DE-588)4002498-2 s Cambridge tracts in mathematics 93 (DE-604)BV000000001 93 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001638755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pinkus, Allan 1946- On L1-approximation Cambridge tracts in mathematics Approximation, Théorie de l' ram théorie approximation inriac Approximation theory Least absolute deviations (Statistics) Beste Approximation (DE-588)4144932-0 gnd Approximation (DE-588)4002498-2 gnd Kleinste absolute Abweichung (DE-588)4501130-8 gnd Approximationstheorie (DE-588)4120913-8 gnd L1-Approximation (DE-588)4449479-8 gnd Čebyšev-Raum (DE-588)4147436-3 gnd |
| subject_GND | (DE-588)4144932-0 (DE-588)4002498-2 (DE-588)4501130-8 (DE-588)4120913-8 (DE-588)4449479-8 (DE-588)4147436-3 |
| title | On L1-approximation |
| title_auth | On L1-approximation |
| title_exact_search | On L1-approximation |
| title_full | On L1-approximation Allan M. Pinkus |
| title_fullStr | On L1-approximation Allan M. Pinkus |
| title_full_unstemmed | On L1-approximation Allan M. Pinkus |
| title_short | On L1-approximation |
| title_sort | on l1 approximation |
| topic | Approximation, Théorie de l' ram théorie approximation inriac Approximation theory Least absolute deviations (Statistics) Beste Approximation (DE-588)4144932-0 gnd Approximation (DE-588)4002498-2 gnd Kleinste absolute Abweichung (DE-588)4501130-8 gnd Approximationstheorie (DE-588)4120913-8 gnd L1-Approximation (DE-588)4449479-8 gnd Čebyšev-Raum (DE-588)4147436-3 gnd |
| topic_facet | Approximation, Théorie de l' théorie approximation Approximation theory Least absolute deviations (Statistics) Beste Approximation Approximation Kleinste absolute Abweichung Approximationstheorie L1-Approximation Čebyšev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001638755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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