Download or read book Jacobi Series and the Numerical Solution of Eigenvalue Problems written by Berthold Schweizer and published by . This book was released on 1956 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.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 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 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 Fractional Dynamics Recent Advances written by Joseph Klafter and published by World Scientific. This book was released on 2011-10-14 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject.In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
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 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 The Symmetric Eigenvalue Problem written by Beresford N. Parlett and published by SIAM. This book was released on 1980-01-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book The Numerical Solution of Elliptic Equations written by Garrett Birkhoff and published by SIAM. This book was released on 1971-01-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.
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 A Jacobi Davidson Type Method for a Right Definite Two parameter Eigenvalue Problem written by Michiel Hochstenbach and published by . This book was released on 2001 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new numerical iterative method for computing selected eigenpairs of a right definite two-parameter eigenvalue problem. The method works even without good initial approximations and is able to tackle large problems that are too expensive for existing methods. The new method is similar to the Jacobi-Davidson method for the eigenvalue problem. In each step we first compute Ritz pairs of a small projected right definite two-parameters eigenvalue problem and then expand the search spaces using approximate solutions of appropriate correction equations. We present two alternatives for the correction equations, introduce a selection technique that makes it possible to compute more than one eigenpair, and give some numerical results.
Download or read book Matrix Algorithms written by G. W. Stewart and published by SIAM. This book was released on 2001-08-30 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. It treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. The notes and reference sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. These volumes are not intended to be encyclopedic, but provide the reader with the theoretical and practical background to read the research literature and implement or modify new algorithms.
Download or read book Jacobi Davidson Methods for Generalized MHD eigenvalue Problems written by J. G. C. Booten and published by . This book was released on 1995 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem Ax=[lambda]Bx is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The method is an inner-outer iterative scheme, in which the inner iteration process consists of solving linear systems to some accuracy. The factorization of either matrix is avoided. Numerical experiments are presented for problems arising in magnetohydrodynamics (MHD)."
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications
Download or read book Lectures on Numerical Mathematics written by H. Rutishauser and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is an edition of the manuscripts to the courses "Numerical Methods I" and "Numerical Mathematics I and II" which Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named course was newly conceived in the spring semester of 1970, and intended for beginners, while the two others were given repeatedly as elective courses in the sixties. For an understanding of most chapters the funda mentals of linear algebra and calculus suffice. In some places a little complex variable theory is used in addition. However, the reader can get by without any knowledge of functional analysis. The first seven chapters discuss the direct solution of systems of linear equations, the solution of nonlinear systems, least squares prob lems, interpolation by polynomials, numerical quadrature, and approxima tion by Chebyshev series and by Remez' algorithm. The remaining chapters include the treatment of ordinary and partial differential equa tions, the iterative solution of linear equations, and a discussion of eigen value problems. In addition, there is an appendix dealing with the qd algorithm and with an axiomatic treatment of computer arithmetic.
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.
