Matrix Perturbation Theory
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Matrix Perturbation Theory
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Author : G. W. Stewart
language : en
Publisher: Academic Press
Release Date : 1990-06-28
Matrix Perturbation Theory written by G. W. Stewart and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-06-28 with Computers categories.
This book is a comprehensive survey of matrix perturbation theory, a topic of interest to numerical analysts, statisticians, physical scientists, and engineers. In particular, the authors cover perturbation theory of linear systems and least square problems, the eignevalue problem, and the generalized eignevalue problem as wellas a complete treatment of vector and matrix norms, including the theory of unitary invariant norms.
Perturbation Theory For Matrix Equations
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Author : M. Konstantinov
language : en
Publisher: Gulf Professional Publishing
Release Date : 2003-05-20
Perturbation Theory For Matrix Equations written by M. Konstantinov and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-20 with Mathematics categories.
The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis. In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds. Key features: • The first book in this field • Can be used by a variety of specialists • Material is self-contained • Results can be used in the development of reliable computational algorithms • A large number of examples and graphical illustrations are given • Written by prominent specialists in the field
The Matrix Perturbation Method In Quantum Mechanics
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Author : Francisco Soto-Eguibar
language : en
Publisher: Springer Nature
Release Date : 2024-02-20
The Matrix Perturbation Method In Quantum Mechanics written by Francisco Soto-Eguibar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-20 with Science categories.
This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.
Analytic Perturbation Theory For Matrices And Operators
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Author : Baumgärtel
language : en
Publisher: Springer
Release Date : 1985
Analytic Perturbation Theory For Matrices And Operators written by Baumgärtel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Juvenile Nonfiction categories.
Analytic Perturbation Theory For Matrices And Operators
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Author : H. Baumgärtel
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1984-12-31
Analytic Perturbation Theory For Matrices And Operators written by H. Baumgärtel and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Mathematics categories.
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Perturbation Bounds For Matrix Eigenvalues
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Author : Rajendra Bhatia
language : en
Publisher: SIAM
Release Date : 1987-01-01
Perturbation Bounds For Matrix Eigenvalues written by Rajendra Bhatia and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Eigenvalues categories.
Perturbation Bounds for Matrix Eigenvalues contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to special classes. The book emphasizes sharp estimates, general principles, elegant methods, and powerful techniques. For the SIAM Classics edition, the author has added over 60 pages of new material, which includes recent results and discusses the important advances made in the theory, results, and proof techniques of spectral variation problems in the two decades since the book's original publication. Audience: physicists, engineers, computer scientists, and mathematicians interested in operator theory, linear algebra, and numerical analysis. The text is also suitable for a graduate course in linear algebra or functional analysis.
Perturbation Theory For Linear Operators
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Author : Tosio Kato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Perturbation Theory For Linear Operators written by Tosio Kato 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 2013-06-29 with Mathematics categories.
Perturbation Theory Of Eigenvalue Problems
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Author : Franz Rellich
language : en
Publisher: CRC Press
Release Date : 1969
Perturbation Theory Of Eigenvalue Problems written by Franz Rellich and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Analytic Perturbation Theory For Matrices And Operators
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Author : Hellmut Baumgärtel
language : en
Publisher: Birkhauser
Release Date : 1985-04
Analytic Perturbation Theory For Matrices And Operators written by Hellmut Baumgärtel and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-04 with Linear operators categories.
Perturbation Methods In Matrix Analysis And Control
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Author : Mihail M. Konstantinov
language : en
Publisher: Nova Science Publishers
Release Date : 2020-04-06
Perturbation Methods In Matrix Analysis And Control written by Mihail M. Konstantinov and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-06 with Control theory categories.
Notation and preliminaries -- Perturbation problems -- Splitting operators and Lyapunov majorants -- Schur decomposition -- Hamiltonian matrices : basic relations -- Hamiltonian matrices : asymptotic analysis -- Hamiltonian matrices : non-local analysis -- Orthogonal canonical forms -- Feedback synthesis problem.