Perturbation Bounds for Matrix Eigenvalues
Perturbation Bounds for Matrix Eigenvalues

Author: Rajendra Bhatia

Publisher: SIAM

Published: 1987-01-01

Total Pages: 191

ISBN-13: 9780898719079

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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.

Perturbation Bounds for Matrix Eigenvalues
Perturbation Bounds for Matrix Eigenvalues

Author: Rajendra Bhatia

Publisher: SIAM

Published: 2007-07-19

Total Pages: 200

ISBN-13: 0898716314

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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.

Matrix Perturbation Theory
Matrix Perturbation Theory

Author: G. W. Stewart

Publisher: Academic Press

Published: 1990-06-28

Total Pages: 392

ISBN-13:

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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 for Matrix Equations
Perturbation Theory for Matrix Equations

Author: M. Konstantinov

Publisher: Gulf Professional Publishing

Published: 2003-05-20

Total Pages: 443

ISBN-13: 0080538673

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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
Perturbation Bounds for the Definite Generalized Eigenvalue Problem

Author: G. W. Stewart

Publisher:

Published: 1977

Total Pages: 26

ISBN-13:

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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.

Numerical Methods for Large Eigenvalue Problems
Numerical Methods for Large Eigenvalue Problems

Author: Yousef Saad

Publisher: SIAM

Published: 2011-01-01

Total Pages: 292

ISBN-13: 9781611970739

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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.

The Theory of Matrices in Numerical Analysis
The Theory of Matrices in Numerical Analysis

Author: Alston S. Householder

Publisher: Courier Corporation

Published: 2013-06-18

Total Pages: 274

ISBN-13: 0486145638

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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.

Numerical Methods for General and Structured Eigenvalue Problems
Numerical Methods for General and Structured Eigenvalue Problems

Author: Daniel Kressner

Publisher: Springer Science & Business Media

Published: 2006-01-20

Total Pages: 272

ISBN-13: 3540285024

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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.