Antieigenvalue analysis: with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 229-240) and index |
| Physical Description: | XIV, 244 S. graph. Darst. 24 cm |
| ISBN: | 9789814366281 9814366285 |
Staff View
MARC
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| 245 | 1 | 0 | |a Antieigenvalue analysis |b with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization |c Karl Gustafson |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2012 | |
| 300 | |a XIV, 244 S. |b graph. Darst. |c 24 cm | ||
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| 650 | 4 | |a Trigonometrical functions | |
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Record in the Search Index
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| adam_text | Titel: Antieigenvalue analysis
Autor: Gustafson, Karl
Jahr: 2012
Contents
Preface ix
1. Introduction 1
Perspective 1
1.1 A Recent Referee Speaks..................... 2
1.2 The Original Motivation..................... 2
1.3 The Essential Entities....................... 3
1.4 Simple Examples and a Picture................. 6
1.5 Applications to-Date....................... 9
1.6 Organization of this Book.................... 10
Commentary 12
1.7 Exercises.............................. 14
2. The Original Motivation: Operator Semigroups 15
Perspective 15
2.1 Abstract Initial Value Problems................. 16
2.2 The Hille-Yosida-Phillips-Lumer Theorem.......... 17
2.3 The Rellich-Kato-Nelson-Gustafson Theorem........ 17
2.4 The Multiplicative Perturbation Theorem........... 18
2.5 When are Positive Operator Products Positive?........ 20
2.6 Nonnegative Contraction Semigroups............. 21
XI
xii Antieigenvalue Analysis
Commentary 22
2.7 Exercises.............................. 23
3. The Essentials of Antieigenvalue Theory 25
Perspective 25
3.1 Convexity Properties of Norm Geometry ........... 26
3.2 The Min-Max Theorem...................... 27
3.3 The Euler Equation........................ 33
3.4 Higher Antieigenvalues and Antieigenvectors ........ 39
3.5 The Triangle Inequality...................... 46
3.6 Extended Operator Trigonometry................ 47
Commentary 49
3.7 Exercises.............................. 50
4. Applications in Numerical Analysis 53
Perspective 53
4.1 Gradient Descent: Kantorovich Bound is Trigonometrie ... 54
4.2 Minimum Residual Ax - b Solvers............... 56
4.3 Richardson Relaxation Schemes (e.g. SOR)........... 57
4.4 Very Rieh Trigonometry Underlies ADI ............ 60
4.5 Domain Decomposition Multilevel Schemes.......... 61
4.6 Preconditioning and Condition Numbers........... 63
Commentary 65
4.7 Exercises.............................. 67
5. Applications in Wavelets, Control, Scattering 69
Perspective 69
5.1 The Time Operator of Wavelets................. 70
5.2 Frame Operator Trigonometry.................. 74
5.3 Wavelet Reconstruction is Trigonometrie............ 76
5.4 New Basis Trigonometry..................... 78
Contents xiii
5.5 Trigonometry of Lyapunov Stability.............. 85
5.6 Multiplicative Perturbation and Irreversibility ........ 86
Commentary 88
5.7 Exercises.............................. 89
6. The Trigonometry of Matrix Statistics 91
Perspective 91
6.1 Statistical Efficiency........................ 91
6.2 The Euler Equation versus the Inefficiency Equation..... 101
6.3 Canonical Correlations and Rayleigh Quotients........ 105
6.4 Other Statistics Inequalities ................... 107
6.5 Prediction Theory: Association Measures ........... 112
6.6 Antieigenmatrices......................... 115
Commentary 116
6.7 Exercises.............................. 118
7. Quantum Trigonometry 123
Perspective 123
7.1 Bell-Wigner-CHSH Inequalities................. 125
7.2 Trigonometrie Quantum Spin Identities............ 129
7.3 Quantum Computing: Phase Issues............... 132
7.4 Penrose Twistors ......................... 135
7.5 Elementary Particles ....................... 142
7.6 Trigonometry of Quantum States................ 144
Commentary 152
7.7 Exercises.............................. 1
8. Financial Instruments 155
Perspective 155
8.1 Some Remarks on Mathematical Finance............ 161
xiv Antieigenvalue Analysis
8.2 Quantos: Currency Options................... 167
8.3 Multi-Asset Pricing: Spread Options.............. 172
8.4 Portfolio Rebalancing....................... 175
8.5 American Options with Random Volatility........... 177
8.6 Risk Measures for Incomplete Markets............. 179
Commentary 181
8.7 Exercises.............................. 182
9. Other Directions 183
Perspective 183
9.1 Operators.............................. 183
9.2 Angles ............................... 186
9.3 Optimization............................ 189
9.4 Equalities.............................. 191
9.5 Geometry.............................. 194
9.6 Applications............................ 199
Commentary 200
9.7 Exercises.............................. 200
Appendix A Linear Algebra 203
A.1 Matrix Analysis.......................... 203
A.2 Operator Theory.......................... 204
Appendix B Hints and Answers to Exercises 205
Bibliography 229
Index 241
|
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| id | DE-604.BV040235172 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:19:38Z |
| institution | BVB |
| isbn | 9789814366281 9814366285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025091491 |
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| physical | XIV, 244 S. graph. Darst. 24 cm |
| publishDate | 2012 |
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| publisher | World Scientific |
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| spelling | Gustafson, Karl 1935- Verfasser (DE-588)15179927X aut Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization Karl Gustafson New Jersey [u.a.] World Scientific 2012 XIV, 244 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 229-240) and index Mathematical analysis Trigonometrical functions Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wavelet (DE-588)4215427-3 s Statistik (DE-588)4056995-0 s Quantenmechanik (DE-588)4047989-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025091491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gustafson, Karl 1935- Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization Mathematical analysis Trigonometrical functions Quantenmechanik (DE-588)4047989-4 gnd Wavelet (DE-588)4215427-3 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4215427-3 (DE-588)4056995-0 |
| title | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization |
| title_auth | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization |
| title_exact_search | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization |
| title_full | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization Karl Gustafson |
| title_fullStr | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization Karl Gustafson |
| title_full_unstemmed | Antieigenvalue analysis with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization Karl Gustafson |
| title_short | Antieigenvalue analysis |
| title_sort | antieigenvalue analysis with applications to numerical analysis wavelets statistics quantum mechanics finance and optimization |
| title_sub | with applications to numerical analysis, wavelets, statistics, quantum mechanics, finance and optimization |
| topic | Mathematical analysis Trigonometrical functions Quantenmechanik (DE-588)4047989-4 gnd Wavelet (DE-588)4215427-3 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical analysis Trigonometrical functions Quantenmechanik Wavelet Statistik |
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