Perturbation Theory For Matrix Equations

Author : M. Konstantinov,D. Wei Gu,V. Mehrmann,P. Petkov
Publisher : Gulf Professional Publishing
Page : 443 pages
File Size : 55,8 Mb
Release : 2003-05-20
Category : Mathematics
ISBN : 9780080538679

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Perturbation Theory for Matrix Equations by M. Konstantinov,D. Wei Gu,V. Mehrmann,P. Petkov Pdf

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

Author : G. W. Stewart,Ji-guang Sun
Publisher : Academic Press
Page : 392 pages
File Size : 41,8 Mb
Release : 1990-06-28
Category : Computers
ISBN : UOM:49015002550854

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Matrix Perturbation Theory by G. W. Stewart,Ji-guang Sun Pdf

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.

Author : Francisco Soto-Eguibar,Braulio Misael Villegas-Martínez,Héctor Manuel Moya-Cessa
Publisher : Springer Nature
Page : 201 pages
File Size : 40,8 Mb
Release : 2024-02-20
Category : Science
ISBN : 9783031485466

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The Matrix Perturbation Method in Quantum Mechanics by Francisco Soto-Eguibar,Braulio Misael Villegas-Martínez,Héctor Manuel Moya-Cessa Pdf

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.

Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257004

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A Short Introduction to Perturbation Theory for Linear Operators by Tosio Kato Pdf

This book is a slightly expanded reproduction of the first two chapters (plus Introduction) of my book Perturbation Theory tor Linear Operators, Grundlehren der mathematischen Wissenschaften 132, Springer 1980. Ever since, or even before, the publication of the latter, there have been suggestions about separating the first two chapters into a single volume. I have now agreed to follow the suggestions, hoping that it will make the book available to a wider audience. Those two chapters were intended from the outset to be a comprehen sive presentation of those parts of perturbation theory that can be treated without the topological complications of infinite-dimensional spaces. In fact, many essential and. even advanced results in the theory have non trivial contents in finite-dimensional spaces, although one should not forget that some parts of the theory, such as those pertaining to scatter ing. are peculiar to infinite dimensions. I hope that this book may also be used as an introduction to linear algebra. I believe that the analytic approach based on a systematic use of complex functions, by way of the resolvent theory, must have a strong appeal to students of analysis or applied mathematics, who are usually familiar with such analytic tools.

Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 54,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662126783

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Perturbation theory for linear operators by Tosio Kato Pdf

Author : James A. Murdock
Publisher : SIAM
Page : 358 pages
File Size : 40,8 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 1611971098

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Perturbations by James A. Murdock Pdf

Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of "uniformity" is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved. First published in 1991, this book is still useful today because it is an introduction. It combines perturbation results with those known through other methods. Sometimes a geometrical result (such as the existence of a periodic solution) is rigorously deduced from a perturbation result, and at other times a knowledge of the geometry of the solutions is used to aid in the selection of an effective perturbation method. Dr. Murdock's approach differs from other introductory texts because he attempts to present perturbation theory as a natural part of a larger whole, the mathematical theory of differential equations. He explores the meaning of the results and their connections to other ways of studying the same problems.

Author : Rajendra Bhatia
Publisher : SIAM
Page : 191 pages
File Size : 54,9 Mb
Release : 1987-01-01
Category : Eigenvalues
ISBN : 0898719070

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Perturbation Bounds for Matrix Eigenvalues by Rajendra Bhatia Pdf

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.

Author : V.N. Bogaevski,A. Povzner
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461244387

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Algebraic Methods in Nonlinear Perturbation Theory by V.N. Bogaevski,A. Povzner Pdf

Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. Topics covered include: matrix perturbation theory; systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives. While boundary problems are not discussed, the book is clearly illustrated by numerous examples.

Author : H. Baumgärtel
Publisher : Walter de Gruyter GmbH & Co KG
Page : 428 pages
File Size : 42,8 Mb
Release : 1984-12-31
Category : Mathematics
ISBN : 9783112721810

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Analytic Perturbation Theory for Matrices and Operators by H. Baumgärtel Pdf

No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".

Author : James G. Simmonds,James E. Mann, Jr.
Publisher : Courier Corporation
Page : 162 pages
File Size : 41,8 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 9780486675510

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A First Look at Perturbation Theory by James G. Simmonds,James E. Mann, Jr. Pdf

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.

Author : Donald R. Smith
Publisher : Cambridge University Press
Page : 532 pages
File Size : 51,8 Mb
Release : 1985-08-30
Category : Mathematics
ISBN : 0521300428

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Singular-Perturbation Theory by Donald R. Smith Pdf

Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.

Author : Antonio Degasperis,Giuseppe Gaeta
Publisher : World Scientific
Page : 338 pages
File Size : 54,8 Mb
Release : 1999-12-30
Category : Electronic
ISBN : 9789814543163

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Symmetry And Perturbation Theory: Spt 98 by Antonio Degasperis,Giuseppe Gaeta Pdf

The second workshop on “Symmetry and Perturbation Theory” served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely.This volume contains tutorial, regular and contributed papers. The tutorial papers give students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.

Author : Giampaolo Cicogna,Guiseppe Gaeta
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 52,9 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540488743

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Symmetry and Perturbation Theory in Nonlinear Dynamics by Giampaolo Cicogna,Guiseppe Gaeta Pdf

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.

Author : Kailash Kumar
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 51,7 Mb
Release : 2017-09-20
Category : Science
ISBN : 9780486825809

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Perturbation Theory and the Nuclear Many Body Problem by Kailash Kumar Pdf

Introductory treatment provides overview of basics and diagrammatic methods. Topics include rearrangement methods and techniques of solving the t-matrix and other equations that arise in the nuclear many body problem. 1962 edition.

Author : Peter Lancaster,Miron Tismenetsky
Publisher : Academic Press
Page : 590 pages
File Size : 55,9 Mb
Release : 1985-05-28
Category : Computers
ISBN : 0124355609

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The Theory of Matrices by Peter Lancaster,Miron Tismenetsky Pdf

Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.