ANTIEIGENVALUE ANALYSIS

With Applications To Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance And Optimization

By: GUSTAFSON KARL

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Hardcover | 27 December 2011

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260 Pages

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22.86 x 15.24 x 1.6

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Karl Gustafson is the creator of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance.Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.

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Preface	p. ix
Introduction	p. 1
Perspective	p. 1
A Recent Referee Speaks	p. 2
The Original Motivation	p. 2
The Essential Entities	p. 3
Simple Examples and a Picture	p. 6
Applications to-Date	p. 9
Organization of this Book	p. 10
Commentary	p. 12
Exercises	p. 14
The Original Motivation: Operator Semigroups	p. 15
Perspective	p. 15
Abstract Initial Value Problems	p. 16
The Hille-Yosida-Phillips-Lumer Theorem	p. 17
The Rellich-Kato-Nelson-Gustafson Theorem	p. 17
The Multiplicative Perturbation Theorem	p. 18
When are Positive Operator Products Positive?	p. 20
Nonnegative Contraction Semigroups	p. 21
Commentary	p. 22
Exercises	p. 23
The Essentials of Antieigenvalue Theory	p. 25
Perspective	p. 25
Convexity Properties of Norm Geometry	p. 26
The Min-Max Theorem	p. 27
The Euler Equation	p. 33
Higher Antieigenvalues and Antieigenvectors	p. 39
The Triangle Inequality	p. 46
Extended Operator Trigonometry	p. 47
Commentary	p. 49
Exercises	p. 50
Applications in Numerical Analysis	p. 53
Perspective	p. 53
Gradient Descent: Kantorovich Bound is Trigonometric	p. 54
Minimum Residual Ax = b Solvers	p. 56
Richardson Relaxation Schemes (e.g. SOR)	p. 57
Very Rich Trigonometry Underlies ADI	p. 60
Domain Decomposition Multilevel Schemes	p. 61
Preconditioning and Condition Numbers	p. 63
Commentary	p. 55
Exercises	p. 67
Applications in Wavelets, Control, Scattering	p. 69
Perspective	p. 59
The Time Operator of Wavelets	p. 70
Frame Operator Trigonometry	p. 74
Wavelet Reconstruction is Trigonometric	p. 76
New Basis Trigonometry	p. 78
Trigonometry of Lyapunov Stability	p. 85
Multiplicative Perturbation and Irreversibility	p. 86
Commentary	p. 88
Exercises	p. 89
The Trigonometry of Matrix Statistics	p. 91
Perspective	p. 91
Statistical Efficiency	p. 91
The Euler Equation versus the Inefficiency Equation	p. 101
Canonical Correlations and Rayleigh Quotients	p. 105
Other Statistics Inequalities	p. 107
Prediction Theory: Association Measures	p. 112
Antieigenmatrices	p. 115
Commentary	p. 116
Exercises	p. 118
Quantum Trigonometry	p. 123
Perspective	p. 123
Bell-Wigner-CHSH Inequalities	p. 125
Trigonometric Quantum Spin Identities	p. 129
Quantum Computing: Phase Issues	p. 132
Penrose Twisters	p. 135
Elementary Particles	p. 142
Trigonometry of Quantum States	p. 144
Commentary	p. 152
Exercises	p. 153
Financial Instruments	p. 155
Perspective	p. 155
Some Remarks on Mathematical Finance	p. 161
Quantos: Currency Options	p. 167
Multi-Asset Pricing: Spread Options	p. 172
Portfolio Rebalancing	p. 175
American Options with Random Volatility	p. 177
Risk Measures for Incomplete Markets	p. 179
Commentary	p. 181
Exercises	p. 182
Other Directions	p. 183
Perspective	p. 183
Operators	p. 183
Angles	p. 186
Optimization	p. 189
Equalities	p. 191
Geometry	p. 194
Applications	p. 199
Commentary	p. 200
Exercises	p. 200
Linear Algebra	p. 203
Matrix Analysis	p. 203
Operator Theory	p. 204
Hints and Answers to Exercises	p. 205
Bibliography	p. 229
Index	p. 241
Table of Contents provided by Ingram. All Rights Reserved.

ANTIEIGENVALUE ANALYSIS

With Applications To Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance And Optimization

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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