Perturbation Theory for the Definite Generalized Eigenvalue Problem PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Perturbation Theory for the Definite Generalized Eigenvalue Problem PDF full book. Access full book title Perturbation Theory for the Definite Generalized Eigenvalue Problem by G. W. Stewart. Download full books in PDF and EPUB format.
Author: G. W. Stewart
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Get Book Here
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.
Author: G. W. Stewart
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Get Book Here
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.
Author: G. W. Stewart
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
Get Book Here
Book Description
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.
Author: G. W. Stewart
Publisher: Academic Press
ISBN:
Category : Computers
Languages : en
Pages : 392
Get Book Here
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.
Author: Gina E. Miner
Publisher:
ISBN:
Category : MATLAB.
Languages : en
Pages : 212
Get Book Here
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.
Author: Franz Rellich
Publisher: CRC Press
ISBN: 9780677006802
Category : Mathematics
Languages : en
Pages : 144
Get Book Here
Book Description
Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
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.
Author: Alston S. Householder
Publisher: Courier Corporation
ISBN: 0486145638
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
This text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations and finding characteristic roots. Topics include norms, bounds and convergence; localization theorems; more. 1964 edition.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Get Book Here
Book Description
Author: Daniel Kressner
Publisher: Springer Science & Business Media
ISBN: 3540285024
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
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.
Author: G. W. Stewart
Publisher: SIAM
ISBN: 0898715032
Category : Mathematics
Languages : en
Pages : 489
Get Book Here
Book Description
This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.
