Iterative methods for the solution of linear systems

Cover of: Iterative methods for the solution of linear systems |

Published by North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co. in Amsterdam, New York, New York, NY, U.S.A .

Written in English

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Subjects:

  • Iterative methods (Mathematics),
  • Linear systems.

Edition Notes

Book details

Statementedited by A. Hadjidimos.
ContributionsHadjidimos, A.
Classifications
LC ClassificationsQA297.8 .I84 1988
The Physical Object
Pagination291 p. :
Number of Pages291
ID Numbers
Open LibraryOL2056970M
ISBN 100444872779
LC Control Number88035484

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Linear algebra, and the central ideas of direct methods for the numerical solution of dense linear systems as described in standard texts such as [7], [],or[]. Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a finite-dimensional setting, weFile Size: KB.

iterative methods for linear systems have made good progress in scientific an d engi- neering disciplines. This is due in great part to the increased complexity and size of.

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. Publisher Summary. This chapter discusses the application of linear stationary iterative method for solving boundary value problem involving an elliptic partial differential equation may lead to a linear system Au = b.

It describes six basic linear stationary iterative methods, which are completely consistent under very general conditions. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from Iterative methods for the solution of linear systems book methods.

Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. Here is a book that focuses on the analysis of iterative methods for solving linear systems. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and by: Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods.

This second edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations, including a wide range of the best /5(9).

This book is also available in Postscript and PDF from these sources: TITLE = {Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition}, PUBLISHER = {SIAM}, YEAR = {}, ADDRESS = {Philadelphia, PA} } Send.

In recent years much research has focused on the efficient solution of large sparse or structured linear systems using iterative methods. A language full of acronyms for a thousand different algorithms has developed, and it is often difficult for the nonspecialist (or sometimes even the specialist) to identify the basic principles involved.

The field of iterative methods for solving systems of linear equations is in constant flux, with new methods and approaches continually being created, modified, tuned, and some eventually discarded. We expect the material in this book to undergo changes from time to time as some of these new approaches mature and become the by: 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.4/5(1).

Iterative methods for solving general, large sparse linear systems have been gaining popularity in many areas of scientific computing. Until recently, direct solution methods were often preferred to iterative methods in real applications because of their robustness and predictable by: In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method.

INTRODUCTION TO DIRECT AND ITERATIVE METHOD Many important practical problems give rise to systems of linear equations written as the matrix equation Ax = c, where A is a given n A— nnonsingular matrix and c is an n-dimensional vector; the problem is to find an n-dimensional vector x satisfying equation.

Such systems of linear equations arise mainly from discrete. Iterative methods for linear systems of equations: A brief historical journey Yousef Saad Abstract.

This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the rst known method that can be termed iterative.

The early 20th century saw good progress of. Purchase Iterative Solution of Large Linear Systems - 1st Edition. Print Book & E-Book.

ISBNThis 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 Cited by: SECTION ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS Theorem Convergence of the Jacobi and Gauss-Seidel Methods If A is strictly diagonally dominant, then the system of linear equations given by has a unique solution to which the Jacobi method and the Gauss-Seidel method will con-verge for any initial approximation.

Ax bFile Size: KB. Iterative methods for solving linear systems October October Read More Cooperative concurrent asynchronous computation of the solution of symmetric linear systems, Numerical Algorithms, which is a vital part of an iterative method.

I recommend the book as a compact but very readable description of the state of the art. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Iterative Solution of Large Linear Systems.

Iterative Solution of Large Linear Systems - Ebook written by David M. Young. Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods.

A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods.

“Iterative Algorithms for Large Sparse Linear Systems on Parallel Computers,” Ph.D. dissertation, Applied Mathematics, University of Virginia; also published as NASA CR Cited by: 3.

The systems of linear equations are a classic section of numerical methods which was already known BC. It reached its highest peak around due to the public demand for solutions of. COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite coefficient matrix.

Using these two operators, we proposed two iterative methods for computing exact solution of linear interval systems. The first method, based on the conjugate gradient method, replaced real operations with interval operations. The second method uses steepest descent idea to solve linear interval systems.

Iterative methods formally yield the solution x of a linear system after an infinite number of steps. At each step they require the computation of the residual of the system. In the case of a full matrix, their computational cost is therefore of the order of n 2 operations for each iteration, to be compared with an overall cost of the order of Cited by: 1.

Saad’s book focuses on iterative methods for the solution of large sparse systems of equations that typically arise in the solution of partial differential equations. The book begins with three introductory chapters that provide background in linear algebra, discretization of partial differential equations, and sparse matrices.

Get this from a library. Iterative Krylov Methods for Large Linear Systems. [Henk A Van der Vorst] -- 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 SOLUTION OF LINEAR SYSTEMS use the following notation: II IIc2 = d& = Euclidean norm of c, II IICB =A/Pz = B-norm of c, if B is Hermitian positive definite, X(B) =the set of eigenvalues of B, Lx(B) =the largest eigenvalue of B, if B is Hermitian, X&(B) =the smallest eigenvalue of B, if B is Hermitian.

Moreover, we denote by In the 71 x n identity matrix; if the dimension 7t. 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. 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 Edition: 1.

Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. This book is written for computational scientists who would like to incorporate state-of-the-art computational methods for solving large sparse systems of linear equations.

Discussions of convergence and stopping criteria, tuning, and selection of method are. Direct methods for solving the linear systems with the Gauss elimination method is given byCarl Friedrich Gauss ().

Thereafter the Choleski gives method for symmetric positive definite matrices. Ø Iterative methods for non-linear equations. The Newton_Raphson method is an iterative method to solve nonlinear equations.

The method is. Iterative methods for the numerical solution of linear systems Maria Louka ⋆ National and Kapodistrian University of Athens Department of Informatics and Telecommunications [email protected] Abstract.

The objective of this dissertation is the design and analysis of iterative methods for the numerical solution of large, sparse linear Size: KB. Synopsis This self-contained treatment offers a systematic development of the theory of iterative methods.

Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. Iterative Methods for Sparse Linear Systems by Yousef Saad.

Publisher: PWS ISBN/ASIN: Description: The book gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number.

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 : Henk A.

van der Vorst. 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. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

When to use iterative methods for solving systems of linear equation. Ask Question Asked 4 years, 11 so you can apply them anywhere where a numerical solution is acceptable. $\endgroup$ – AlexR May 26 '. T1 - Remarks on iterative methods for the solution of large systems of linear algebraic equations.

AU - Widlund, Olof. PY - Y1 - M3 - Conference contribution. BT - Proceedings of the NRCC Conference, Santa Cruz, AugustER -Author: Olof Widlund. M.R. Hestenes, Historical papers: Iterative methods for solving linear equations, JOTA 11 (), – and The solution of linear equations by minimization, JOTA 11 (), – Completed on Decem The first paper originally appeared as NAML Report No.Cited by:   Abstract.

Conjugate gradient is an iterative method that solves a linear system, where is a positive definite matrix.

We present this new iterative method for solving linear interval systems, where is a diagonally dominant interval matrix, as defined in this paper.

Our method is based on conjugate gradient algorithm in the context view of interval by: 2.

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