Noisy information and computational complexity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1996
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 308 S. |
| ISBN: | 0521553687 |
Staff View
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Record in the Search Index
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| adam_text | NOISY INFORMATION AND COMPUTATIONAL COMPLEXITY LESZEK PLASKOTA INSTITUTE
OF APPLIED MATHEMATICS AND MECHANICS UNIVERSITY OF WARSAW WARSAW, POLAND
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX LIST OF SYMBOLS X 1
OVERVIEW 1 2 WORST CASE SETTING 5 2.1 INTRODUCTION 5 2.2 INFORMATION,
ALGORITHMS, APPROXIMATION 8 2.3 RADIUS AND DIAMETER OF INFORMATION 12
2.4 AFFINE ALGORITHMS FOR LINEAR FUNCTIONAL 20 2.4.1 EXISTENCE OF
OPTIMAL AFFINE ALGORITHMS 20 2.4.2 THE CASE OF HILBERT NOISE 23 2.5
OPTIMALITY OF SPLINE ALGORITHMS 32 2.5.1 SPLINES AND SMOOTHING SPLINES
32 2.5.2 A-SMOOTHING SPLINES 35 2.6 SPECIAL SPLINES 44 2.6.1 THE HUBERT
CASE WITH OPTIMAL A 44 2.6.2 LEAST SQUARES AND REGULARIZATIOH 50 2.6.3
POLYNOMIAL SPLINES 54 2.6.4 SPLINES IN R.K.H.S. 58 2.7 VARYING
INFORMATION 63 2.7.1 NONADAPTIVE AND ADAPTIVE INFORMATION 63 2.7.2 WHEN
DOES ADAPTION NOT HELP? 66 2.8 OPTIMAL NONADAPTIVE INFORMATION 71 2.8.1
LINEAR PROBLEMS IN HILBERT SPACES 71 2.8.2 APPROXIMATION AND INTEGRATION
OF LIPSCHITZ FUNCTIONS 81 2.9 COMPLEXITY 89 2.9.1 COMPUTATIONS OVER THE
SPACE G 89 2.9.2 COST AND COMPLEXITY, GENERAL BOUNDS 92 VI CONTENTS 2.10
COMPLEXITY OF SPECIAL PROBLEMS 100 2.10.1 LINEAR PROBLEMS IN HILBERT
SPACES 100 2.10.2 APPROXIMATION AND INTEGRATION OF LIPSCHITZ FUNCTIONS
106 2.10.3 MULTIVARIATE APPROXIMATION IN A BANACH SPACE 109 3 AVERAGE
CASE SETTING 121 3.1 INTRODUCTION 121 3.2 INFORMATION AND ITS RADIUS 123
3.3 GAUSSIAN MEASURES ON BANACH SPACES 132 3.3.1 BASIC PROPERTIES 132
3.3.2 GAUSSIAN MEASURES AS ABSTRACT WIENER SPACES 134 3.4 LINEAR
PROBLEMS WITH GAUSSIAN MEASURES 139 3.4.1 INDUCED AND CONDITIONAL
DISTRIBUTIONS 140 3.4.2 OPTIMAL ALGORITHMS 143 3.5 THE CASE OF LINEAR
FUNCTIONAL 148 3.6 OPTIMAL ALGORITHMS AS SMOOTHING SPLINES 155 3.6.1 A
GENERAL CASE 156 3.6.2 SPECIAL CASES 157 3.6.3 RELATIONS TO WORST CASE
SETTING 159 3.7 VARYING INFORMATION 162 3.7.1 NONADAPTIVE AND ADAPTIVE
INFORMATION 163 3.7.2 ADAPTION VERSUS NONADAPTION 165 3.8 OPTIMAL
NONADAPTIVE INFORMATION 170 3.8.1 LINEAR PROBLEMS WITH GAUSSIAN MEASURES
170 3.8.2 APPROXIMATION AND INTEGRATION ON THE WIENER SPACE 180 3.9
COMPLEXITY 197 3.9.1 ADAPTION VERSUS NONADAPTION 198 3.9.2 COMPLEXITY
BOUNDS 202 3.10 COMPLEXITY OF SPECIAL PROBLEMS 205 3.10.1 LINEAR
PROBLEMS WITH GAUSSIAN MEASURES 205 3.10.2 APPROXIMATION AND INTEGRATION
ON THE WIENER SPACE 210 4 WORST-AVERAGE CASE SETTING 215 4.1
INTRODUCTION 215 4.2 AFFINE ALGORITHMS FOR LINEAR FUNCTIONAL 216 4.2.1
THE ONE DIMENSIONAL PROBLEM 216 4.2.2 ALMOST OPTIMALITY OF AFFINE
ALGORITHMS 220 4.2.3 RELATIONS TO OTHER SETTINGS 230 4.3 APPROXIMATION
OF OPERATORS 234 4.3.1 ELLIPSOIDAL PROBLEMS IN R N 234 4.3.2 THE HILBERT
CASE 238 CONTENTS VII 5 AVERAGE-WORST CASE SETTING 248 5.1 INTRODUCTION
248 5.2 LINEAR ALGORITHMS FOR LINEAR FUNCTIONALS- 249 5.2.1 THE ONE
DIMENSIONAL PROBLEM 249 5.2.2 ALMOST OPTIMALITY OF LINEAR ALGORITHMS 252
5.2.3 RELATIONS TO OTHER SETTINGS 260 5.3 APPROXIMATION OF OPERATORS 263
6 ASYMPTOTIC SETTING 268 6.1 INTRODUCTION 268 6.2 ASYMPTOTIC AND WORST
CASE SETTINGS 269 6.2.1 INFORMATION, ALGORITHM AND ERROR 270 6.2.2
OPTIMAL ALGORITHMS 271 6.2.3 OPTIMAL NONADAPTIVE INFORMATION 276 6.3
ASYMPTOTIC AND AVERAGE CASE SETTINGS 281 6.3.1 OPTIMAL ALGORITHMS 282
6.3.2 CONVERGENCE RATE 285 6.3.3 OPTIMAL NONADAPTIVE INFORMATION 288
REFERENCES 293 AUTHOR INDEX 304 SUBJECT INDEX 306
|
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| discipline | Informatik Elektrotechnik |
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| indexdate | 2024-07-09T17:59:40Z |
| institution | BVB |
| isbn | 0521553687 |
| language | English |
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| physical | XI, 308 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Cambridge Univ. Press |
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| spelling | Plaskota, Leszek Verfasser aut Noisy information and computational complexity Leszek Plaskota 1. publ. Cambridge Cambridge Univ. Press 1996 XI, 308 S. txt rdacontent n rdamedia nc rdacarrier Computational complexity Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Partielle Information (DE-588)4232570-5 gnd rswk-swf Partielle Information (DE-588)4232570-5 s Berechnungskomplexität (DE-588)4134751-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007240671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Plaskota, Leszek Noisy information and computational complexity Computational complexity Berechnungskomplexität (DE-588)4134751-1 gnd Partielle Information (DE-588)4232570-5 gnd |
| subject_GND | (DE-588)4134751-1 (DE-588)4232570-5 |
| title | Noisy information and computational complexity |
| title_auth | Noisy information and computational complexity |
| title_exact_search | Noisy information and computational complexity |
| title_full | Noisy information and computational complexity Leszek Plaskota |
| title_fullStr | Noisy information and computational complexity Leszek Plaskota |
| title_full_unstemmed | Noisy information and computational complexity Leszek Plaskota |
| title_short | Noisy information and computational complexity |
| title_sort | noisy information and computational complexity |
| topic | Computational complexity Berechnungskomplexität (DE-588)4134751-1 gnd Partielle Information (DE-588)4232570-5 gnd |
| topic_facet | Computational complexity Berechnungskomplexität Partielle Information |
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