Author: Gina E. Miner
Publisher:
ISBN:
Category : MATLAB.
Languages : en
Pages : 212
Book Description
" ... 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.
Matrix Perturbation Theory as Applied to the Classical and Generalized Eigenvalue Problems
Author: Gina E. Miner
Publisher:
ISBN:
Category : MATLAB.
Languages : en
Pages : 212
Book Description
" ... 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.
Publisher:
ISBN:
Category : MATLAB.
Languages : en
Pages : 212
Book Description
" ... 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.
Perturbation Theory for the Definite Generalized Eigenvalue Problem
Author: G. W. Stewart
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
This paper concerns perturbation theory for the generalized eigenvalue problem Ax = lambdaBx where A and B are real symmetric matrices of order n> or = to 3. When B is positive definite, as is usually the case in applications, the problem can be reduced to a symmetric eigenvalue problem for the matrix square root of B times the square root of AB, and the wealth of perturbation theory for symmetric eigenvalue problems can be applied.
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
This paper concerns perturbation theory for the generalized eigenvalue problem Ax = lambdaBx where A and B are real symmetric matrices of order n> or = to 3. When B is positive definite, as is usually the case in applications, the problem can be reduced to a symmetric eigenvalue problem for the matrix square root of B times the square root of AB, and the wealth of perturbation theory for symmetric eigenvalue problems can be applied.
Numerical Methods for Large Eigenvalue Problems
Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Matrix Perturbation Theory
Author: G. W. Stewart
Publisher: Academic Press
ISBN:
Category : Computers
Languages : en
Pages : 392
Book Description
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.
Publisher: Academic Press
ISBN:
Category : Computers
Languages : en
Pages : 392
Book Description
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 of Eigenvalue Problems
Author: Franz Rellich
Publisher: CRC Press
ISBN: 9780677006802
Category : Mathematics
Languages : en
Pages : 144
Book Description
Publisher: CRC Press
ISBN: 9780677006802
Category : Mathematics
Languages : en
Pages : 144
Book Description
Numerical Methods for General and Structured Eigenvalue Problems
Author: Daniel Kressner
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Book Description
This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Book Description
This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Perturbation Theory for Matrix Equations
Author: M. Konstantinov
Publisher: Gulf Professional Publishing
ISBN: 0080538673
Category : Mathematics
Languages : en
Pages : 443
Book Description
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
Publisher: Gulf Professional Publishing
ISBN: 0080538673
Category : Mathematics
Languages : en
Pages : 443
Book Description
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
Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610
Book Description
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610
Book Description
Perturbation Bounds for Matrix Eigenvalues
Author: Rajendra Bhatia
Publisher: SIAM
ISBN: 0898716314
Category : Mathematics
Languages : en
Pages : 200
Book Description
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.
Publisher: SIAM
ISBN: 0898716314
Category : Mathematics
Languages : en
Pages : 200
Book Description
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 of Eigenvalue Problems (Classic Reprint)
Author: F. Rellich
Publisher: Forgotten Books
ISBN: 9780331809268
Category : Mathematics
Languages : en
Pages : 348
Book Description
Excerpt from Perturbation Theory of Eigenvalue Problems Power series in Hilbert Space Perturbation of an isolated eigenvalue of finite multiplicity of a bounded Operator Essentially self-adjoint, and self-adjoint. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Publisher: Forgotten Books
ISBN: 9780331809268
Category : Mathematics
Languages : en
Pages : 348
Book Description
Excerpt from Perturbation Theory of Eigenvalue Problems Power series in Hilbert Space Perturbation of an isolated eigenvalue of finite multiplicity of a bounded Operator Essentially self-adjoint, and self-adjoint. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.