Perturbation Bounds For Matrix Eigenvalues
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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.
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 Bounds For Matrix Eigenvalues
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Author : Rajendra Bhatia
language : en
Publisher: SIAM
Release Date : 2007-07-19
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 2007-07-19 with Mathematics categories.
For the SIAM Classics edition, the author has added over 60 pages of material covering recent results and discussing the important advances made in the last two decades. It is an excellent research reference for all those interested in operator theory, linear algebra, and numerical analysis.
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 Bounds For The Definite Generalized Eigenvalue Problem
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Author : G. W. Stewart
language : en
Publisher:
Release Date : 1977
Perturbation Bounds For The Definite Generalized Eigenvalue Problem written by G. W. Stewart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
It is shown that a definite problem has a complete system of eigenvectors and its eigenvalues are real. Under perturbations of A and B, the eigenvalues behave like the eigenvalues of a Hermitian matrix in the sense that there is a 1-1 pairing of the eigenvalues with the perturbed eigenvalues and a uniform bound for their differences (in this case in the chordal metric). Perturbation bounds are also developed for eigenvectors and eigenspaces.
Bounds For The Eigenvalues Of A Matrix
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Author : Kenneth R. Garren
language : en
Publisher:
Release Date : 1968
Bounds For The Eigenvalues Of A Matrix written by Kenneth R. Garren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Eigenvalues categories.
Matrix Perturbation Theory As Applied To The Classical And Generalized Eigenvalue Problems
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Author : Gina E. Miner
language : en
Publisher:
Release Date : 1989
Matrix Perturbation Theory As Applied To The Classical And Generalized Eigenvalue Problems written by Gina E. Miner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with MATLAB. categories.
" ... a survey of perturbation bounds on several quantities of interest in matrix eigenanalysis ... In addition ... a software facility for analyzing perturbations has been developed using MATLAB, [which facility] is described."--Abstract.
Optimal Perturbation Bounds For The Hermitian Eigenvalue Problem
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Author : Jesse Louis Barlow
language : en
Publisher:
Release Date : 1999
Optimal Perturbation Bounds For The Hermitian Eigenvalue Problem written by Jesse Louis Barlow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Eigenvalues categories.
Abstract: "There is now a large literature on structured perturbation bounds for eigenvalue problems of the form [formula], where H and M are Hermitian. These results give relative error bounds on the i[superscript th] eigenvalue, [lambda subscript i], of the form [formula], and bound the error in the i[superscript th] eigenvector in terms of the relative gap, [formula]. In general, this theory usually restricts H to be nonsingular and M to be positive definite. We relax this restriction by allowing H to be singular. For our results on eigenvales we allow M to be positive semi-definite and for few results we allow it to be more general. For these problems, for eigenvalues that are not zero or infinity under perturbation, it is possible to obtain local relative error bounds. Thus, a wider class of problems may be characterized by this theory. The theory is applied to the SVD and some of its generalizations. In fact, for structured perturbations, our bound on generalized Hermitian eigenproblems are based upon our bounds for generalized singular value problems. Although it is impossible to give meaningful relative error bounds on eigenvalues that are not bounded away from zero, we show that the error in the subspace associated with those eigenvalues can be characterized meaningfully."
Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications
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Author : A. Weinstein
language : en
Publisher: Elsevier
Release Date : 1972-06-23
Methods Of Intermediate Problems For Eigenvalues Theory And Ramifications written by A. Weinstein and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-23 with Mathematics categories.
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
The Symmetric Eigenvalue Problem
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Author : Beresford N. Parlett
language : en
Publisher: SIAM
Release Date : 1998-01-01
The Symmetric Eigenvalue Problem written by Beresford N. Parlett and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.