Novel Computational Methods For Eigenvalue Problems
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Novel Computational Methods For Eigenvalue Problems
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Author :
language : en
Publisher:
Release Date : 2019
Novel Computational Methods For Eigenvalue Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Abstract : This dissertation focuses on novel computational method for eigenvalue problems. In Chapter 1, preliminaries of functional analysis related to eigenvalue problems are presented. Some classical methods for matrix eigenvalue problems are discussed. Several PDE eigenvalue problems are covered. The chapter is concluded with a summary of the contributions. In Chapter 2, a novel recursive contour integral method (RIM) for matrix eigenvalue problem is proposed. This method can effectively find all eigenvalues in a region on the complex plane with no a priori spectrum information. Regions that contain eigenvalues are subdivided and tested recursively until the size of region reaches specified precision. The method is robust, which is demonstrated using various examples. In Chapter 3, we propose an improved version of RIM for non-Hermitian eigenvalue problems, called SIM-M. By incorporating Cayley transformation and Arnoldi's method, the main computation cost of solving linear systems is reduced significantly. The numerical experiments demonstrate that RIM-M gains significant speed-up over RIM. In Chapter 4, we propose a multilevel spectral indicator method (SIM-M) to address the memory requirement for large sparse matrices. We modify the indicator of RIM-M such that it requires much less memory. Matrices from University of Florida Sparse Matrix Collection are tested, suggesting that a parallel version of SIM-M has the potential to be efficient. In Chapter 5, we develop a novel method to solve the elliptic PDE eigenvalue problem. We construct a multi-wavelet basis with Riesz stability in H1 0 ( ). By incorporating multi-grid discretization scheme and sparse grids, the method retains the optimal convergence rate for the smallest eigenvalue with much less computational cost.
Novel Computational Methods For Solving High Dimensional Random Eigenvalue Problems
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Author : Vaibhav Yadav
language : en
Publisher:
Release Date : 2013
Novel Computational Methods For Solving High Dimensional Random Eigenvalue Problems written by Vaibhav Yadav and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Eigenvalues categories.
When the cooperative effects of input variables on an eigenvalue attenuate rapidly or vanish altogether, the PDD approximation commits smaller error than does the PCE approximation for identical expansion orders. Numerical analysis reveal higher convergence rates and significantly higher efficiency of the PDD approximation than the PCE approximation. Second, two novel multiplicative PDD methods, factorized PDD and logarithmic PDD, were developed to exploit the hidden multiplicative structure of an REP, if it exists. Since a multiplicative PDD recycles the same component functions of the additive PDD, no additional cost is incurred. Numerical results show that indeed both the multiplicative PDD methods are capable of effectively utilizing the multiplicative structure of a random response.
Numerical Methods For Large Eigenvalue Problems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2011-05-26
Numerical Methods For Large Eigenvalue Problems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
This revised edition discusses numerical methods for computing the 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.
Numerical Methods For General And Structured Eigenvalue Problems
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Author : Daniel Kressner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20
Numerical Methods For General And Structured Eigenvalue Problems written by Daniel Kressner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Mathematics categories.
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.
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems
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Author : Xuefeng Liu
language : en
Publisher: Springer Nature
Release Date :
Guaranteed Computational Methods For Self Adjoint Differential Eigenvalue Problems written by Xuefeng Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Computational Methods Of Linear Algebra 3rd Edition
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Author : Granville Sewell
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-07-07
Computational Methods Of Linear Algebra 3rd Edition written by Granville Sewell and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Mathematics categories.
This book presents methods for the computational solution of some important problems of linear algebra: linear systems, linear least squares problems, eigenvalue problems, and linear programming problems. The book also includes a chapter on the fast Fourier transform and a very practical introduction to the solution of linear algebra problems on modern supercomputers.The book contains the relevant theory for most of the methods employed. It also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs for solving linear algebraic problems. Highly readable FORTRAN and MATLAB codes are presented which solve all of the main problems studied.
Spectral Methods For Non Standard Eigenvalue Problems
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Author : Călin-Ioan Gheorghiu
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22
Spectral Methods For Non Standard Eigenvalue Problems written by Călin-Ioan Gheorghiu and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Mathematics categories.
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.
Computational Methods For Integral Equations
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Author : L. M. Delves
language : en
Publisher: Cambridge University Press
Release Date : 1985-10-31
Computational Methods For Integral Equations written by L. M. Delves and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-10-31 with Mathematics categories.
Integral equations form an important class of problems, arising frequently in engineering, and in mathematical and scientific analysis. This textbook provides a readable account of techniques for their numerical solution. The authors devote their attention primarily to efficient techniques using high order approximations, taking particular account of situations where singularities are present. The classes of problems which arise frequently in practice, Fredholm of the first and second kind and eigenvalue problems, are dealt with in depth. Volterra equations, although attractive to treat theoretically, arise less often in practical problems and so have been given less emphasis. Some knowledge of numerical methods and linear algebra is assumed, but the book includes introductory sections on numerical quadrature and function space concepts. This book should serve as a valuable text for final year undergraduate or postgraduate courses, and as an introduction or reference work for practising computational mathematicians, scientists and engineers.
Finite Element Methods For Eigenvalue Problems
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Author : Jiguang Sun
language : en
Publisher: CRC Press
Release Date : 2016-08-19
Finite Element Methods For Eigenvalue Problems written by Jiguang Sun and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.
The Formulation And Analysis Of Numerical Methods For Inverse Eigenvalue Problems
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Author : S Friedland
language : en
Publisher: Legare Street Press
Release Date : 2023-07-18
The Formulation And Analysis Of Numerical Methods For Inverse Eigenvalue Problems written by S Friedland and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with categories.
Inverse eigenvalue problems are among the most challenging and important topics in computational mathematics. This rigorous and accessible text offers a comprehensive introduction to the formulation and analysis of numerical methods for solving these problems, including a detailed discussion of the mathematical theory behind the methods and practical examples of their application. Whether you're a graduate student or an active researcher in the field, this book is an essential resource for mastering the latest techniques in inverse eigenvalue computation. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.