Download or read book The Symmetric Eigenvalue Problem written by Beresford N. Parlett and published by SIAM. This book was released on 1998-01-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.

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 The Matrix Eigenvalue Problem written by David S. Watkins and published by SIAM. This book was released on 2007-01-01 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth, theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems.

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 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 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 Large Scale Eigenvalue Problems written by J. Cullum and published by Elsevier. This book was released on 1986-01-01 with total page 329 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 An Introduction to Random Matrices written by Greg W. Anderson and published by Cambridge University Press. This book was released on 2010 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Download or read book Linear Algebra for Large Scale and Real Time Applications written by M.S. Moonen and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3-14, 1992

Download or read book Applied Numerical Linear Algebra written by James W. Demmel and published by SIAM. This book was released on 1997-08-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

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 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 Random Eigenvalue Problems written by Jürgen Vom Scheidt and published by North-Holland. This book was released on 1983 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Element Methods for Eigenvalue Problems written by Jiguang Sun and published by CRC Press. This book was released on 2016-08-19 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Core Chasing Algorithms for the Eigenvalue Problem written by Jared L. Aurentz and published by SIAM. This book was released on 2018-07-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenvalue computations are ubiquitous in science and engineering. John Francis’s implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm. While Francis’s original procedure chases bulges, the new version chases core transformations, which allows the development of fast algorithms for eigenvalue problems with a variety of special structures. This also leads to a fast and backward stable algorithm for computing the roots of a polynomial by solving the companion matrix eigenvalue problem. The authors received a SIAM Outstanding Paper prize for this work. This book will be of interest to researchers in numerical linear algebra and their students.

Download or read book Lanczos Algorithms for Large Symmetric Eigenvalue Computations Vol I Theory written by CULLUM and published by Birkhäuser. This book was released on 2012-05-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy levels, resonanees, vibrations, feature extraetion, faetor analysis - the names vary from discipline to diseipline; however, all involve eigenvalue/eigenveetor eomputations. An engineer or physicist who is modeling a physieal proeess, strueture, or deviee is eonstrained to seleet a model for whieh the subsequently-required eomputations ean be performed. This eonstraint often leads to redueed order or redueed size models whieh may or may not preserve all of the important eharaeteristies of the system being modeled. Ideally, the modeler should not be foreed to make such apriori reduetions. It is our intention to provide here proeedures wh ich will allow the direct and suceessful solution of many large 'symmetrie' eigenvalue problems, so that at least in problems where the computations are of this type there will be no need for model reduetion. Matrix eigenelement eomputations can be c1assified as smalI, medium, or large seale, in terms of their relative degrees of difficulty as measured by the amount of computer storage and time required to eomplete the desired eomputations. A matrix eigenvalue problem is said to be sm all scale if the given matrix has order smaller than 100. Well-documented and reliable FORTRAN pro grams exist for small scale eigenelement computations, see in particular ElS­ PACK [1976,1977]. Typically those programs explicitly trans form the given matrix into a simpler canonieal form. The eigenelement eomputations are then performed on the canonical form.