On the Inversion of Eigenvalue Problems PDF Download

Author: Egil Andersen Hylleraas
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 24

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Author: Moody Chu
Publisher: Oxford University Press
ISBN: 0198566646
Category : Mathematics
Languages : en
Pages : 408

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Book Description
Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.

Author: Egil Andersen Hylleraas
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 19

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Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292

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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 Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.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: Fioralba Cakoni
Publisher: SIAM
ISBN: 1611974461
Category : Mathematics
Languages : en
Pages : 200

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Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance.? Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues.? The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.?

Author: Moody Ten-Chao Chu
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: S. Friedland
Publisher: Forgotten Books
ISBN: 9780656185153
Category : Mathematics
Languages : en
Pages : 64

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Excerpt from The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems Both the additive and multiplicative inverse eigenvalue problems were posed by Down ing and Householder In practical applications of the inverse sturm-liouville and inverse vibrating string problems, only a few of the smallest eigenvalues may be given. In order for the problem to be well-posed, the number of parameters must be reduced accordingly. This can be done by expressing the potential or density function as a linear combination of a few given basis functions. See Osborne (1971) and Hald (1972) for details. 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.

Author: Steffen Börm
Publisher: Walter de Gruyter
ISBN: 3110250373
Category : Mathematics
Languages : en
Pages : 216

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Eigenvalues and eigenvectors of matrices and linear operators play an important role when solving problems from structural mechanics and electrodynamics, e.g., by describing the resonance frequencies of systems, when investigating the long-term behavior of stochastic processes, e.g., by describing invariant probability measures, and as a tool for solving more general mathematical problems, e.g., by diagonalizing ordinary differential equations or systems from control theory. This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behavior with the goal to present an easily accessible introduction to the field, including rigorous proofs of all important results, but not a complete overview of the vast body of research. Several programming examples allow the reader to experience the behavior of the different algorithms first-hand. The book addresses students and lecturers of mathematics, physics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve new problems.

Author: Shu-fang Xu
Publisher: Springer
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 320

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Book Description
Algebraische Inverse Eigenwertprobleme behandeln die Frage, wie man die Elemente einer Matrix aus den Spektralwerten bestimmen kann. Dies ist ein zentrales Thema in vielen Problemkreisen (z. B. Kontrolltheorie, Molekularspektroskopie, Geologie).

Author: S Friedland
Publisher: Andesite Press
ISBN: 9781297828126
Category :
Languages : en
Pages : 60

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Book Description
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