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Author : David S. Watkins
Publisher : SIAM
Page : 443 pages
File Size : 53,9 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898716412
An in-depth, theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems.
Author : Yousef Saad
Publisher : SIAM
Page : 292 pages
File Size : 41,9 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 1611970733
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 Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.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.
Author : Daniel Kressner
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 49,6 Mb
Release : 2006-01-20
Category : Mathematics
ISBN : 9783540285021
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.
Author : Steffen Börm,Christian Mehl
Publisher : Walter de Gruyter
Page : 216 pages
File Size : 55,7 Mb
Release : 2012-05-29
Category : Mathematics
ISBN : 9783110250374
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.
Author : David S. Watkins
Publisher : SIAM
Page : 452 pages
File Size : 49,7 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717809
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.
Author : Beresford N. Parlett
Publisher : SIAM
Page : 422 pages
File Size : 44,5 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 1611971160
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.
Author : Moody Chu,Gene Golub
Publisher : Oxford University Press
Page : 408 pages
File Size : 43,8 Mb
Release : 2005-06-16
Category : Mathematics
ISBN : 9780198566649
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.
Author : Kenneth Kuttler,Ilijas Farah
Publisher : Unknown
Page : 586 pages
File Size : 47,6 Mb
Release : 2020
Category : Algebras, Linear
ISBN : OCLC:1252786692
"A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.
Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 53,6 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9783319050898
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
Author : Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Publisher : SIAM
Page : 430 pages
File Size : 41,5 Mb
Release : 2000-01-01
Category : Computers
ISBN : 9780898714715
Mathematics of Computing -- Numerical Analysis.
Author : Federico Milano,Ioannis Dassios,Muyang Liu,Georgios Tzounas
Publisher : CRC Press
Page : 407 pages
File Size : 55,6 Mb
Release : 2020-12-22
Category : Technology & Engineering
ISBN : 9781000335200
The book provides a comprehensive taxonomy of non-symmetrical eigenvalues problems as applied to power systems. The book bases all formulations on mathematical concept of “matrix pencils” (MPs) and considers both regular and singular MPs for the eigenvalue problems. Each eigenvalue problem is illustrated with a variety of examples based on electrical circuits and/or power system models and controllers and related data are provided in the appendices of the book. Numerical methods for the solution of all considered eigenvalue problems are discussed. The focus is on large scale problems and, hence, attention is dedicated to the performance and scalability of the methods. The target of the book are researchers and graduated students in Electrical & Computer Science Engineering, both taught and research Master programmes as well as PhD programmes and it: explains eigenvalue problems applied into electrical power systems explains numerical examples on applying the mathematical methods, into studying small signal stability problems of realistic and large electrical power systems includes detailed and in-depth analysis including non-linear and other advanced aspects provides theoretical understanding and advanced numerical techniques essential for secure operation of power systems provides a comprehensive set of illustrative examples that support theoretical discussions
Author : John Lund
Publisher : Unknown
Page : 308 pages
File Size : 49,7 Mb
Release : 2010-09-14
Category : Education
ISBN : 0757584926
Author : Jiguang Sun,Aihui Zhou
Publisher : CRC Press
Page : 368 pages
File Size : 47,5 Mb
Release : 2016-08-19
Category : Mathematics
ISBN : 9781482254655
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.
Author : Jared L. Aurentz,Thomas Mach,Leonardo Robol,Raf Vandebril,David S. Watkins
Publisher : SIAM
Page : 155 pages
File Size : 53,6 Mb
Release : 2018-07-06
Category : Science
ISBN : 9781611975338
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.
Author : Moody Chu,Gene Golub
Publisher : OUP Oxford
Page : 406 pages
File Size : 53,7 Mb
Release : 2005-06-16
Category : Mathematics
ISBN : 0198566646
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.