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Author : H. A. van der Vorst
Publisher : Cambridge University Press
Page : 242 pages
File Size : 53,6 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 0521818281
Table of contents
Author : Henk A. van der Vorst
Publisher : Cambridge University Press
Page : 0 pages
File Size : 48,6 Mb
Release : 2009-10-01
Category : Mathematics
ISBN : 0521183707
Based on extensive research by Henk van der Vorst, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. Van der Vorst demonstrates how these methods can be derived from basic iteration formulas and how they are related. Focusing on the ideas behind the methods rather than a complete presentation of the theory, the volume includes a substantial amount of references for further reading as well as exercises to help students initially encountering the material.
Author : H. A. van der Vorst
Publisher : Unknown
Page : 0 pages
File Size : 41,7 Mb
Release : 2003
Category : Electronic
ISBN : OCLC:892288210
Author : Yousef Saad
Publisher : SIAM
Page : 537 pages
File Size : 48,9 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347
Mathematics of Computing -- General.
Author : Gérard Meurant,Jurjen Duintjer Tebbens
Publisher : Springer Nature
Page : 686 pages
File Size : 51,5 Mb
Release : 2020-10-02
Category : Mathematics
ISBN : 9783030552510
This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.
Author : David R. Kincaid,Linda J. Hayes
Publisher : Academic Press
Page : 350 pages
File Size : 49,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260204
Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.
Author : Daniele Bertaccini,Fabio Durastante
Publisher : CRC Press
Page : 366 pages
File Size : 49,9 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351649612
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 257 pages
File Size : 50,7 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464
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.??
Author : Anne Greenbaum
Publisher : SIAM
Page : 225 pages
File Size : 52,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713961
Mathematics of Computing -- Numerical Analysis.
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 : 55,6 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 : Gerard Meurant
Publisher : Elsevier
Page : 777 pages
File Size : 48,9 Mb
Release : 1999-06-16
Category : Mathematics
ISBN : 9780080529516
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.
Author : Are Magnus Bruaset
Publisher : Routledge
Page : 140 pages
File Size : 46,5 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469364
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
Author : Wolfgang Hackbusch
Publisher : Springer
Page : 460 pages
File Size : 52,8 Mb
Release : 1993-12-13
Category : Mathematics
ISBN : 9780387940649
C. F. GauS in a letter from Dec. 26, 1823 to Gerling: 3c~ empfe~le 3~nen biegen IDlobu9 aur 9tac~a~mung. ec~werlic~ werben eie ie wieber bi reet eliminiren, wenigftens nic~t, wenn eie me~r als 2 Unbefannte ~aben. :Da9 inbirecte 93erfa~ren 109st sic~ ~alb im ec~lafe ausfii~ren, ober man fann wo~renb be9gelben an anbere :Dinge benfen. [CO F. GauS: Werke vol. 9, Gottingen, p. 280, 1903] What difference exists between solving large and small systems of equations? The standard methods well-known to any student oflinear algebra are appli cable to all systems, whether large or small. The necessary amount of work, however, increases dramatically with the size, so one has to search for algo rithms that most efficiently and accurately solve systems of 1000, 10,000, or even one million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretisation of partial differential equations. In this case, the matrices are sparse (i. e. , they contain mostly zeros) and well-suited to iterative algorithms. Because of the background in partial differential equa tions, this book is closely connected with the author's Theory and Numerical Treatment of Elliptic Differential Equations, whose English translation has also been published by Springer-Verlag. This book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics.
Author : Are Magnus Bruaset
Publisher : Routledge
Page : 175 pages
File Size : 40,8 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469371
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
Author : David E. Keyes,Ahmed Sameh,V. Venkatakrishnan
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401154123
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.
