Author: Gabriele Ciaramella
Publisher: SIAM
ISBN: 1611976901
Category : Mathematics
Languages : en
Pages : 285
Get Book Here
Book Description
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.
Author: Are Magnus Bruaset
Publisher: Routledge
ISBN: 1351469363
Category : Mathematics
Languages : en
Pages : 140
Get Book Here
Book Description
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: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
Get Book Here
Book Description
Mathematics of Computing -- General.
Author: Daniele Bertaccini
Publisher: CRC Press
ISBN: 1351649612
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
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: H. A. van der Vorst
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
Get Book Here
Book Description
Table of contents
Author: Owe Axelsson
Publisher: Cambridge University Press
ISBN: 9780521555692
Category : Mathematics
Languages : en
Pages : 676
Get Book Here
Book Description
This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
Author: Ke Chen
Publisher: Cambridge University Press
ISBN: 9780521838283
Category : Mathematics
Languages : en
Pages : 616
Get Book Here
Book Description
A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.
Author: Josef Malek
Publisher: SIAM
ISBN: 161197383X
Category : Mathematics
Languages : en
Pages : 106
Get Book Here
Book Description
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?
Author: David J. Evans
Publisher: Gordon & Breach Science Pub
ISBN: 9782881249563
Category : Computers
Languages : en
Pages : 491
Get Book Here
Book Description
Precondition Gradient Methods emerged in the early 1970s as the most impressive algorithm for the large sparse definite problems. The method has gained large acceptance throughout the world since then and undergone rapid development. The method has been generalized to non-symmetric and indefinite problems, domain decomposition, eigenvalue problems, and many other application areas. The analysis of the preconditioning strategy is both a mathematically fascinating and complex topic. Since the topic appears to be expanding in importance, it was felt opportune to present this volume containing papers on preconditioned iterative methods, Incomplete Factorisation and SSOR preconditioning and the Preconditioned Conjugate Gradient Method covering symmetric and non-symmetric systems on computers (vector and parallel) for finite element and computational fluid dynamic applications. This volume serves as a useful companion volume to the previously published "Preconditioning Methods: Theory and Application"
Author: David Ronald Kincaid
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
Very Good,No Highlights or Markup,all pages are intact.
