Perturbation Theory For Matrix Equations
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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
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.
Matrix Theory
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Author : David Lewis
language : en
Publisher: World Scientific Publishing Company
Release Date : 1991-09-30
Matrix Theory written by David Lewis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-30 with Mathematics categories.
This book provides an introduction to matrix theory and aims to provide a clear and concise exposition of the basic ideas, results and techniques in the subject. Complete proofs are given, and no knowledge beyond high school mathematics is necessary. The book includes many examples, applications and exercises for the reader, so that it can used both by students interested in theory and those who are mainly interested in learning the techniques.
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.
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
Introduction To Perturbation Theory In Quantum Mechanics
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Author : Francisco M. Fernandez
language : en
Publisher: CRC Press
Release Date : 2000-09-19
Introduction To Perturbation Theory In Quantum Mechanics written by Francisco M. Fernandez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-19 with Science categories.
Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation “/p>
The Matrix Perturbation Method In Quantum Mechanics
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Author : Francisco Soto-Eguibar
language : en
Publisher: Springer Nature
Release Date : 2024-01-19
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 2024-01-19 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.
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory
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Author : Peter Benner
language : en
Publisher: Springer
Release Date : 2015-05-09
Numerical Algebra Matrix Theory Differential Algebraic Equations And Control Theory written by Peter Benner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-09 with Mathematics categories.
This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Perturbation Techniques In Mathematics Engineering And Physics
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Author : Richard Ernest Bellman
language : en
Publisher: Courier Corporation
Release Date : 2003-01-01
Perturbation Techniques In Mathematics Engineering And Physics written by Richard Ernest Bellman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Science categories.
Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.
Analytic Perturbation Theory For Matrices And Operators
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Author : H. Baumgärtel
language : en
Publisher: de Gruyter
Release Date : 1984-12-31
Analytic Perturbation Theory For Matrices And Operators written by H. Baumgärtel and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-31 with Mathematics categories.
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
Scattering Theory Some Old And New Problems
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Author : Dmitri R. Yafaev
language : en
Publisher: Springer
Release Date : 2007-05-06
Scattering Theory Some Old And New Problems written by Dmitri R. Yafaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.