Download or read book Structured Approaches to General Inverse Eigenvalue Problems written by Patrick Dumond and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An inverse eigenvalue problem is one where a set or subset of (generalized) eigenvalues is specified and the matrices that generate it are sought. Many methods for solving inverse eigenvalue problems are only applicable to matrices of a specific type. In this chapter, two recently proposed methods for structured (direct) solutions of inverse eigenvalue problems are presented. The presented methods are not restricted to matrices of a specific type and are thus applicable to matrices of all types. For the first method, the Cayley-Hamilton theorem is developed for the generalized eigenvalue vibration problem. For a given (desired) frequency spectrum, many solutions are possible. Hence, a discussion of the required information and suggestions for including structural constraints are given. An algorithm for solving the inverse eigenvalue problem using the generalized Cayley-Hamilton theorem is then demonstrated. An algorithm for solving partially described systems is also specified. The Cayley-Hamilton theorem algorithm is shown to be a good tool for solving inverse generalized eigenvalue problems. Examples of application of the method are given. A second method, referred to as the inverse eigenvalue determinant method, is also introduced. This method provides another direct approach to the reconstruction of the matrices of the generalized eigenvalue problem, given knowledge of its eigenvalues and various physical parameters. As for the first method, there are no restrictions on the type of matrices allowed for the inverse problem. Examples of application of the method are also given, including application-oriented examples.
Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On Some Structured Inverse Eigenvalue Problems written by Robert Erra and published by . This book was released on 1995 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Linear Algebra in Action written by Vasilios Katsikis and published by BoD – Books on Demand. This book was released on 2016-07-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present text book contains a collection of six high-quality articles. In particular, this book is devoted to Linear Mathematics by presenting problems in Applied Linear Algebra of general or special interest.
Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by OUP Oxford. This book was released on 2005-06-16 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamical Inverse Problems Theory and Application written by Graham M. L. Gladwell and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Download or read book Numerical Methods for Eigenvalue Problems written by Steffen Börm and published by Walter de Gruyter. This book was released on 2012-05-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems Classic Reprint written by S. Friedland and published by Forgotten Books. This book was released on 2018-02-09 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Matrix Eigenvalue Problem written by David S. Watkins and published by SIAM. This book was released on 2007-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
Download or read book Inverse Eigenvalue Problems written by Moody Ten-Chao Chu and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symplectic Methods for the Symplectic Eigenproblem written by Heike Fassbender and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of eigenvalue problems is an integral part of many scientific computations. For example, the numerical solution of problems in structural dynamics, electrical networks, macro-economics, quantum chemistry, and c- trol theory often requires solving eigenvalue problems. The coefficient matrix of the eigenvalue problem may be small to medium sized and dense, or large and sparse (containing many zeroelements). In the past tremendous advances have been achieved in the solution methods for symmetric eigenvalue pr- lems. The state of the art for nonsymmetric problems is not so advanced; nonsymmetric eigenvalue problems can be hopelessly difficult to solve in some situations due, for example, to poor conditioning. Good numerical algorithms for nonsymmetric eigenvalue problems also tend to be far more complex than their symmetric counterparts. This book deals with methods for solving a special nonsymmetric eig- value problem; the symplectic eigenvalue problem. The symplectic eigenvalue problem is helpful, e.g., in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Certain quadratic eigenvalue problems arising, e.g., in finite element discretization in structural analysis, in acoustic simulation of poro-elastic materials, or in the elastic deformation of anisotropic materials can also lead to symplectic eigenvalue problems. The problem appears in other applications as well.
Download or read book Templates for the Solution of Algebraic Eigenvalue Problems written by Zhaojun Bai and published by SIAM. This book was released on 2000-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Computational Methods In Engineering Advances Applications Proceedings Of The International Conference In 2 Volumes written by Khin-yong Lam and published by World Scientific. This book was released on 1992-10-29 with total page 1556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods in Structural Mechanics written by Zdenek Bittnar and published by Thomas Telford. This book was released on 1996-04-05 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed presentation is offered of the fundamental equations in solid mechanics focusing on constitutive equations including quasibrittle materials. Details are provided on individual numerical algorithms, with a heavier emphasis placed on the understanding of basic principles.
Download or read book Numerical Methods and Software for General and Structured Eigenvalue Problems written by Daniel Kreßner and published by . This book was released on 2004 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt:
