Krylov Solvers For Linear Algebraic Systems
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Krylov Solvers For Linear Algebraic Systems
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Author : Charles George Broyden
language : en
Publisher: Elsevier
Release Date : 2004-09-08
Krylov Solvers For Linear Algebraic Systems written by Charles George Broyden and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-08 with Mathematics categories.
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
Krylov Solvers For Linear Algebraic Systems
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Author : Charles George Broyden
language : en
Publisher: Elsevier Science
Release Date : 2004-12-15
Krylov Solvers For Linear Algebraic Systems written by Charles George Broyden and has been published by Elsevier Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-15 with Mathematics categories.
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.
Iterative Methods For Linear Systems
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Author : Maxim A. Olshanskii
language : en
Publisher: SIAM
Release Date : 2014-01-01
Iterative Methods For Linear Systems written by Maxim A. Olshanskii and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Mathematics categories.
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.
Krylov Solvers For Linear Algebraic Systems
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Author : Charles George Broyden
language : en
Publisher:
Release Date : 2004
Krylov Solvers For Linear Algebraic Systems written by Charles George Broyden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebras, Linear categories.
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.
Iterative Methods For Sparse Linear Systems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01
Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.
Mathematics of Computing -- General.
Iterative Krylov Methods For Large Linear Systems
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Author : H. A. van der Vorst
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Iterative Krylov Methods For Large Linear Systems written by H. A. van der Vorst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Parallel Numerical Algorithms
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Author : David E. Keyes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Numerical Algorithms written by David E. Keyes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Iterative Methods For Linear And Nonlinear Equations
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 1995-01-01
Iterative Methods For Linear And Nonlinear Equations written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
A Journey Through The History Of Numerical Linear Algebra
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Author : Claude Brezinski
language : en
Publisher: SIAM
Release Date : 2022-12-06
A Journey Through The History Of Numerical Linear Algebra written by Claude Brezinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
Templates For The Solution Of Linear Systems
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Author : Richard Barrett
language : en
Publisher: SIAM
Release Date : 1994-01-01
Templates For The Solution Of Linear Systems written by Richard Barrett and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.