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Author : Zhaojun Bai,James Demmel,Jack Dongarra,Axel Ruhe,Henk van der Vorst
Publisher : SIAM
Page : 430 pages
File Size : 46,9 Mb
Release : 2000-01-01
Category : Computers
ISBN : 9780898714715
Mathematics of Computing -- Numerical Analysis.
Author : Yousef Saad
Publisher : SIAM
Page : 292 pages
File Size : 53,8 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 Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section.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 : G. W. Stewart
Publisher : SIAM
Page : 489 pages
File Size : 53,8 Mb
Release : 2001-08-30
Category : Mathematics
ISBN : 9780898715033
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.
Author : Daniel Kressner
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 55,9 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 : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 781 pages
File Size : 50,6 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9781421407944
This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.
Author : Steffen Börm,Christian Mehl
Publisher : Walter de Gruyter
Page : 216 pages
File Size : 45,9 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 : Philippe G. Ciarlet,Jacques-Louis Lions
Publisher : Gulf Professional Publishing
Page : 698 pages
File Size : 44,7 Mb
Release : 1990
Category : Mathematics
ISBN : 0444509062
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
Author : Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
Publisher : SIAM
Page : 141 pages
File Size : 53,7 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611971535
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.
Author : Richard B. Lehoucq,Danny C. Sorensen,Chao Yang
Publisher : SIAM
Page : 150 pages
File Size : 54,6 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 9780898714074
This book is a guide to understanding and using the software package ARPACK to solve large algebraic eigenvalue problems. The software described is based on the implicitly restarted Arnoldi method, which has been heralded as one of the three most important advances in large scale eigenanalysis in the past ten years. The book explains the acquisition, installation, capabilities, and detailed use of the software for computing a desired subset of the eigenvalues and eigenvectors of large (sparse) standard or generalized eigenproblems. It also discusses the underlying theory and algorithmic background at a level that is accessible to the general practitioner.
Author : Leslie Hogben
Publisher : CRC Press
Page : 1402 pages
File Size : 54,8 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9781420010572
The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl
Author : Jared L. Aurentz,Thomas Mach,Leonardo Robol,Raf Vandebril,David S. Watkins
Publisher : SIAM
Page : 149 pages
File Size : 48,8 Mb
Release : 2018-07-06
Category : Science
ISBN : 9781611975345
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 : Biswa Nath Datta
Publisher : SIAM
Page : 545 pages
File Size : 42,5 Mb
Release : 2010-02-04
Category : Mathematics
ISBN : 9780898716856
An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.
Author : Erricos John Kontoghiorghes
Publisher : CRC Press
Page : 560 pages
File Size : 41,7 Mb
Release : 2005-12-21
Category : Computers
ISBN : 1420028685
Technological improvements continue to push back the frontier of processor speed in modern computers. Unfortunately, the computational intensity demanded by modern research problems grows even faster. Parallel computing has emerged as the most successful bridge to this computational gap, and many popular solutions have emerged based on its concepts
Author : Åke Björck
Publisher : Springer
Page : 800 pages
File Size : 51,9 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 : Lloyd N. Trefethen,Mark Embree
Publisher : Princeton University Press
Page : 634 pages
File Size : 54,5 Mb
Release : 2005-08-07
Category : Mathematics
ISBN : 0691119465
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
