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Author : H. Baumgärtel
Publisher : Walter de Gruyter GmbH & Co KG
Page : 428 pages
File Size : 49,9 Mb
Release : 1984-12-31
Category : Mathematics
ISBN : 9783112721810
No detailed description available for "Analytic Perturbation Theory for Matrices and Operators".
Author : Baumgärtel
Publisher : Springer
Page : 446 pages
File Size : 46,9 Mb
Release : 1985
Category : Juvenile Nonfiction
ISBN : UCAL:B4128227
Author : Hellmut Baumgärtel
Publisher : Birkhauser
Page : 0 pages
File Size : 40,6 Mb
Release : 1985-04
Category : Linear operators
ISBN : 0817616640
Author : Tosio Kato
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461257004
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 : M. Konstantinov,D. Wei Gu,V. Mehrmann,P. Petkov
Publisher : Gulf Professional Publishing
Page : 443 pages
File Size : 41,6 Mb
Release : 2003-05-20
Category : Mathematics
ISBN : 9780080538679
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 : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 49,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662126783
Author : Konstantin E. Avrachenkov,Jerzy A. Filar,Phil G. Howlett
Publisher : SIAM
Page : 384 pages
File Size : 50,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781611973143
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Author : Aref Jeribi
Publisher : Springer Nature
Page : 509 pages
File Size : 49,6 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9789811625282
This book discusses the important aspects of spectral theory, in particular, the completeness of generalised eigenvectors, Riesz bases, semigroup theory, families of analytic operators, and Gribov operator acting in the Bargmann space. Recent mathematical developments of perturbed non-self-adjoint operators are discussed with the completeness of the space of generalized eigenvectors, bases on Hilbert and Banach spaces and asymptotic behavior of the eigenvalues of these operators. Most results in the book are motivated by physical problems, such as the perturbation method for sound radiation by a vibrating plate in a light fluid, Gribov operator in Bargmann space and other applications in mathematical physics and mechanics. This book is intended for students, researchers in the field of spectral theory of linear non self-adjoint operators, pure analysts and mathematicians.
Author : Mihail M. Konstantinov,Petko Hr Petkov
Publisher : Nova Science Publishers
Page : 281 pages
File Size : 43,8 Mb
Release : 2020-04-06
Category : Control theory
ISBN : 153617470X
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.
Author : Konstantin E. Avrachenkov,Jerzy A. Filar,Phil G. Howlett
Publisher : SIAM
Page : 384 pages
File Size : 47,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781611973136
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Author : G. S. Litvinchuk,I. M. Spitkovskii
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 45,9 Mb
Release : 2022-01-19
Category : Social Science
ISBN : 9783112471722
Author : Franz Rellich
Publisher : CRC Press
Page : 144 pages
File Size : 53,8 Mb
Release : 1969
Category : Mathematics
ISBN : 0677006802
Author : Israel Gohberg,Heinz Langer
Publisher : Birkhäuser
Page : 282 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881814
In September 1998, during the 'International Workshop on Analysis and Vibrat ing Systems' held in Canmore, Alberta, Canada, it was decided by a group of participants to honour Peter Lancaster on the occasion of his 70th birthday with a volume in the series 'Operator Theory: Advances and Applications'. Friends and colleagues responded enthusiastically to this proposal and within a short time we put together the volume which is now presented to the reader. Regarding accep tance of papers we followed the usual rules of the journal 'Integral Equations and Operator Theory'. The papers are dedicated to different problems in matrix and operator theory, especially to the areas in which Peter contributed so richly. At our request, Peter agreed to write an autobiographical paper, which appears at the beginning of the volume. It continues with the list of Peter's publications. We believe that this volume will pay tribute to Peter on his outstanding achievements in different areas of mathematics. 1. Gohberg, H. Langer P ter Lancast r *1929 Operator Theory: Advances and Applications, Vol. 130, 1- 7 © 2001 Birkhiiuser Verlag Basel/Switzerland My Life and Mathematics Peter Lancaster I was born in Appleby, a small county town in the north of England, on November 14th, 1929. I had two older brothers and was to have one younger sister. My family moved around the north of England as my father's work in an insurance company required.
Author : H. Bart,I. Gohberg,Kaashoek
Publisher : Birkhäuser
Page : 383 pages
File Size : 50,5 Mb
Release : 2013-11-22
Category : Science
ISBN : 9783034856720
Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 48,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206538
This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
