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Krylov Solvers For Linear Algebraic Systems
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Book Synopsis Krylov Solvers for Linear Algebraic Systems by : Charles George Broyden
Download or read book Krylov Solvers for Linear Algebraic Systems written by Charles George Broyden and published by Elsevier. This book was released on 2004-09-08 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradientalgorithm. These are the matrix of coefficients and the preconditioningmatrix.In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.·comprehensive and unified approach·up-to-date chapter on preconditioners·complete theory of stability·includes dual and reverse methods·comparison of algorithms on CD-ROM·objective assessment of algorithms
Book Synopsis Krylov Solvers for Linear Algebraic Systems by : Charles George Broyden
Download or read book Krylov Solvers for Linear Algebraic Systems written by Charles George Broyden and published by Elsevier Science. This book was released on 2004-12-29 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. · comprehensive and unified approach · up-to-date chapter on preconditioners · complete theory of stability · includes dual and reverse methods · comparison of algorithms on CD-ROM · objective assessment of algorithms
Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Book Synopsis Iterative Krylov Methods for Large Linear Systems by : H. A. van der Vorst
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Iterative Methods for Linear Systems by : Maxim A. Olshanskii
Download or read book Iterative Methods for Linear Systems written by Maxim A. Olshanskii and published by SIAM. This book was released on 2014-07-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??
Book Synopsis Iterative Methods and Preconditioners for Systems of Linear Equations by : Gabriele Ciaramella
Download or read book Iterative Methods and Preconditioners for Systems of Linear Equations written by Gabriele Ciaramella and published by SIAM. This book was released on 2022-02-08 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.
Book Synopsis Iterative Methods for Solving Linear Systems by : Anne Greenbaum
Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Krylov Solvers for Linear Algebraic Systems by : Charles George Broyden
Download or read book Krylov Solvers for Linear Algebraic Systems written by Charles George Broyden and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of the block conjugate-gradient algorithm and it is this observation that permits the unification of the theory. The two major sub-classes of those methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt algorithm and their properties, in particular their stability properties, are determined by the two matrices that define the block conjugate-gradient algorithm. These are the matrix of coefficients and the preconditioning matrix. In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms. In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM. Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices. comprehensive and unified approach up-to-date chapter on preconditioners complete theory of stability includes dual and reverse methods comparison of algorithms on CD-ROM objective assessment of algorithms.
Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w
Book Synopsis Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers by : Iman Farahbakhsh
Download or read book Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers written by Iman Farahbakhsh and published by John Wiley & Sons. This book was released on 2020-09-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: A succinct and complete explanation of Krylov subspace methods for solving systems of equations Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers is the most current and complete guide to the implementation of Krylov subspace methods for solving systems of equations with different types of matrices. Written in the simplest language possible and eliminating ambiguities, the text is easy to follow for post-grad students and applied mathematicians alike. The book covers a breadth of topics, including: The different methods used in solving the systems of equations with ill-conditioned and well-conditioned matrices The behavior of Krylov subspace methods in the solution of systems with ill-posed singular matrices Expertly supported with the addition of a companion website hosting computer programs of appendices The book includes executable subroutines and main programs that can be applied in CFD codes as well as appendices that support the results provided throughout the text. There is no other comparable resource to prepare the reader to use Krylov subspace methods in incompressible fluid flow solvers.
Book Synopsis Templates for the Solution of Linear Systems by : Richard Barrett
Download or read book Templates for the Solution of Linear Systems written by Richard Barrett and published by SIAM. This book was released on 1994-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parallel Numerical Algorithms by : David E. Keyes
Download or read book Parallel Numerical Algorithms written by David E. Keyes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.
Author :J. J. Dongarra Publisher :Society for Industrial and Applied Mathematics (SIAM) ISBN 13 : Total Pages :274 pages Book Rating :4.3/5 (91 download)
Book Synopsis Solving Linear Systems on Vector and Shared Memory Computers by : J. J. Dongarra
Download or read book Solving Linear Systems on Vector and Shared Memory Computers written by J. J. Dongarra and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 1991 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
Book Synopsis Numerical Methods for Large Eigenvalue Problems by : Yousef Saad
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.
Book Synopsis Iterative Methods for Large Linear Systems by : David Ronald Kincaid
Download or read book Iterative Methods for Large Linear Systems written by David Ronald Kincaid and published by . This book was released on 1990 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Book Synopsis Computer Solution of Large Linear Systems by : Gerard Meurant
Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Book Synopsis Krylov Subspace Methods by : Jörg Liesen
Download or read book Krylov Subspace Methods written by Jörg Liesen and published by Numerical Mathematics and Scie. This book was released on 2013 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.
