Antieigenvalue Analysis
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Antieigenvalue Analysis
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Author : Karl Gustafson
language : en
Publisher: World Scientific
Release Date : 2012
Antieigenvalue Analysis written by Karl Gustafson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Karl Gustafson is the creater 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.
Antieigenvalue Analysis
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Author : Karl Gustafson
language : en
Publisher: World Scientific
Release Date : 2011
Antieigenvalue Analysis written by Karl Gustafson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
1.1. A recent referee speaks. 1.2. The original motivation. 1.3. The essential entities. 1.4. Simple examples and a picture. 1.5. Applications to-date. 1.6. Organization of this book -- 2.1. Abstract initial value problems. 2.2. The Hille-Yosida-Phillips-Lumer theorem. 2.3. The Rellich-Kato-Nelson-Gustafson theorem. 2.4. The multiplicative perturbation theorem. 2.5. When are positive operator products positive?. 2.6. Nonnegative contraction semigroups. 3.1. Convexity properties of norm geometry. 3.2. The min-max theorem. 3.3. The Euler equation. 3.4. Higher antieigenvalues and antieigenvectors. 3.5. The triangle inequality. 3.6. Extended operator trigonometry -- 4. Applications in numerical analysis. 4.1. Gradient descent: Kantorovich bound is trigonometric. 4.2. Minimum residual Ax = b solvers. 4.3. Richardson relaxation schemes (e.g. SOR). 4.4. Very rich trigonometry underlies ADI. 4.5. Domain decomposition multilevel schemes. 4.6. Preconditioning and condition numbers -- 5. Applications in wavelets, control, scattering. 5.1. The time operator of wavelets . 5.2. Frame operator trigonometry. 5.3. Wavelet reconstruction is trigonometric. 5.4. New basis trigonometry. 5.5. Trigonometry of Lyapunov stability. 5.6. Multiplicative perturbation and irreversibility -- 6. The trigonometry of matrix statistics. 6.1. Statistical efficiency. 6.2. The Euler equation versus the inefficiency equation. 6.3. Canonical correlations and Rayleigh quotients. 6.4. Other statistics inequalities. 6.5. Prediction theory: association measures. 6.6. Antieigenmatrices -- 7. Quantum trigonometry. 7.1. Bell-Wigner-CHSH inequalities. 7.2. Trigonometric quantum spin identities. 7.3 Quantum computing: phase issues. 7.4. Penrose twistors. 7.5. Elementary particles. 7.6. Trigonometry of quantum states -- 8. Financial instruments. 8.1. Some remarks on mathematical finance. 8.2. Quantos: currency options. 8.3. Multi-asset pricing: spread options. 8.4. Portfolio rebalancing. 8.5. American options with random volatility. 8.6. Risk measures for incomplete markets -- 9. Other directions. 9.1. Operators. 9.2. Angles. 9.3. Optimization. 9.4. Equalities. 9.5. Geometry. 9.6. Applications
Generalized Functions Operator Theory And Dynamical Systems
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Author : Ioannis Antoniou
language : en
Publisher: CRC Press
Release Date : 2021-02-25
Generalized Functions Operator Theory And Dynamical Systems written by Ioannis Antoniou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.
Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.
Methodology And Applications Of Statistics
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Author : Barry C. Arnold
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Methodology And Applications Of Statistics written by Barry C. Arnold and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Mathematics categories.
Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a bird’s-eye view of a broad spectrum of research topics, paralleling C.R. Rao’s wide-ranging research interests. The book’s contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the book’s original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Computer Vision Accv 2006
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Author : P.J. Narayanan
language : en
Publisher: Springer
Release Date : 2006-01-14
Computer Vision Accv 2006 written by P.J. Narayanan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-14 with Computers categories.
These volumes present together a total of 64 revised full papers and 128 revised posters papers. The papers are organized in topical sections on camera calibration, stereo and pose, texture, face recognition, variational methods, tracking, geometry and calibration, lighting and focus, in the first volume. The papers of the second volume cover topics as detection and applications, statistics and kernels, segmentation, geometry and statistics, signal processing, and video processing.
The Crossing Of Heaven
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Author : Karl Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05
The Crossing Of Heaven written by Karl Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.
Among the group of physics honors students huddled in 1957 on a Colorado mountain watching Sputnik bisect the heavens, one young scientist was destined, three short years later, to become a key player in America’s own top-secret spy satellite program. One of our era’s most prolific mathematicians, Karl Gustafson was given just two weeks to write the first US spy satellite’s software. The project would fundamentally alter America’s Cold War strategy, and this autobiographical account of a remarkable academic life spent in the top flight tells this fascinating inside story for the first time. Gustafson takes you from his early pioneering work in computing, through fascinating encounters with Nobel laureates and Fields medalists, to his current observations on mathematics, science and life. He tells of brushes with death, being struck by lightning, and the beautiful women who have been a part of his journey.
Lectures On Computational Fluid Dynamics Mathematical Physics And Linear Algebra
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Author : Karl E. Gustafson
language : en
Publisher: World Scientific
Release Date : 1997
Lectures On Computational Fluid Dynamics Mathematical Physics And Linear Algebra written by Karl E. Gustafson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Drama categories.
Pt. I. Recent developments in computational fluid dynamics. ch. 1. Cavity flow -- ch. 2. Hovering aerodynamics. ch. 3. Capturing correct solutions -- pt. II. Recent developments in mathematical physics. ch. 1. Probabilistic and deterministic description. ch. 2. Scaling theories. ch. 3. Chaos in iterative maps -- pt. III. Recent developments in linear algebra. ch. 1. Operator Trigonometry. ch. 2. Antieigenvalues. ch. 3. Computational linear algebra
Numerical Range
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Author : Karl E. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Range written by Karl E. Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Matrix Tricks For Linear Statistical Models
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Author : Simo Puntanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-24
Matrix Tricks For Linear Statistical Models written by Simo Puntanen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Mathematics categories.
In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.