Download or read book Multiparameter Eigenvalue Problems Methods and Algorithms written by Bohdan Podlevskyi and published by . This book was released on 2018-01-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Singular Multiparameter Eigenvalue Problems written by Andrej Muhič and published by . This book was released on 2011 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1960s Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems. Many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems are based on this relation. We extend the above relation to singular two-parameter eigenvalue problems and show that the simple finite regular eigenvalues of a two-parameter eigenvalue problem and the common regular eigenvalues of the coupled generalized eigenvalue problem agree. Using the theory on the pencils of matrix polynomials we furthermore generalize the theory to the nonregular singular two-parameter eigenvalue problems. This enables one to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems. There are various numerical methods for twoparameter eigenvalue problems, but all of them can only be applied to nonsingular problems. We develop a numerical method that can be applied to the singular two-parameter eigenvalue problems. It is based on the staircase algorithm for the extraction of the common regular part of two singular matrix pencils. We introduce the quadratic two-parameter eigenvalue problem (QMEP) and show that we can linearize it as a regular singular two-parameter eigenvalue problem. We present several transformations that can be used to solve the QMEP, by formulating an associated linear multiparameter eigenvalue problem. We also generalize the linearization to the polynomial twoparameter eigenvalue problem(PMEP). As an alternative approach to the linearization, we propose the transformation of the QMEP into a nonsingular five-parameter eigenvalue problem. We also consider several special cases of the QMEP, where some matrix coefficients are zero, which allows us to solve such QMEP more efficiently. We propose a Jacobi-Davidson type method for regular singular problems. We modify the Jacobi-Davidson type method for nonsingular two-parameter eigenvalue problem so that it can be applied to regular singular problems. The obtained algorithm can then be used to solve the problem obtained by linearizing the PMEP. If the dimension of matrices is large, then we cannot use the approach with linearization. If order of polynomials is small enough, then we can apply a Jacobi-Davidson type method directly to the polynomial system. This method is a generalization of the method for polynomial eigenvalue problems. We give some numerical results that illustrate the convergence of the introduced Jacobi-Davidson type methods.

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 Y. Saad and published by Manchester University Press. This book was released on 1992 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.

Download or read book Modern Algorithms for Large Sparse Eigenvalue Problems written by Arnd Meyer and published by . This book was released on 1987 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Eigenvalue Problems Algorithms Software and Applications in Petascale Computing written by Tetsuya Sakurai and published by Springer. This book was released on 2018-01-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

Download or read book Large Scale Eigenvalue Problems written by J. Cullum and published by Elsevier. This book was released on 1986-01-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories: novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.

Download or read book Multiparameter eigenvalue problems written by Atkinson and published by Academic Press. This book was released on 1972-06-16 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiparameter eigenvalue problems

Download or read book High Precision Methods in Eigenvalue Problems and Their Applications written by Leonid D. Akulenko and published by CRC Press. This book was released on 2004-10-15 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high

Download or read book Multiparameter Eigenvalue Problems and Expansion Theorems written by Hans Volkmer and published by Springer. This book was released on 2006-11-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained treatment of two of the main problems of multiparameter spectral theory: the existence of eigenvalues and the expansion in series of eigenfunctions. The results are first obtained in abstract Hilbert spaces and then applied to integral operators and differential operators. Special attention is paid to various definiteness conditions which can be imposed on multiparameter eigenvalue problems. The reader is not assumed to be familiar with multiparameter spectral theory but should have some knowledge of functional analysis, in particular of Brower's degree of maps.

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 Multiparameter Eigenvalue Problems written by F.V. Atkinson and published by CRC Press. This book was released on 2010-12-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem

Download or read book Multiparameter Eigenvalue Problems written by F. V. Atkinson and published by . This book was released on 1972-01-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Guaranteed Computational Methods for Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and published by Springer Nature. This book was released on with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods for Non Standard Eigenvalue Problems written by Călin-Ioan Gheorghiu and published by Springer Science & Business. This book was released on 2014-04-22 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.