Iterative Methods And Preconditioning For Large And Sparse Linear Systems With Applications
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Author |
: Daniele Bertaccini |
Publisher |
: CRC Press |
Total Pages |
: 375 |
Release |
: 2018-02-19 |
ISBN-10 |
: 9781498764179 |
ISBN-13 |
: 1498764177 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini
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 |
: Yousef Saad |
Publisher |
: SIAM |
Total Pages |
: 537 |
Release |
: 2003-04-01 |
ISBN-10 |
: 9780898715347 |
ISBN-13 |
: 0898715342 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Mathematics of Computing -- General.
Author |
: Are Magnus Bruaset |
Publisher |
: Routledge |
Total Pages |
: 175 |
Release |
: 2018-12-13 |
ISBN-10 |
: 9781351469371 |
ISBN-13 |
: 1351469371 |
Rating |
: 4/5 (71 Downloads) |
Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset
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 |
Total Pages |
: 546 |
Release |
: 2003-01-01 |
ISBN-10 |
: 0898718007 |
ISBN-13 |
: 9780898718003 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical 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. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
Author |
: Daniele Bertaccini |
Publisher |
: CRC Press |
Total Pages |
: 321 |
Release |
: 2018-02-19 |
ISBN-10 |
: 9781351649612 |
ISBN-13 |
: 1351649612 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini
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 |
Publisher |
: SIAM |
Total Pages |
: 257 |
Release |
: 2014-07-21 |
ISBN-10 |
: 9781611973464 |
ISBN-13 |
: 1611973465 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Iterative Methods for Linear Systems by : Maxim A. Olshanskii
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 |
: H. A. van der Vorst |
Publisher |
: Cambridge University Press |
Total Pages |
: 242 |
Release |
: 2003-04-17 |
ISBN-10 |
: 0521818281 |
ISBN-13 |
: 9780521818285 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Iterative Krylov Methods for Large Linear Systems by : H. A. van der Vorst
Table of contents
Author |
: Anne Greenbaum |
Publisher |
: SIAM |
Total Pages |
: 225 |
Release |
: 1997-01-01 |
ISBN-10 |
: 9780898713961 |
ISBN-13 |
: 089871396X |
Rating |
: 4/5 (61 Downloads) |
Synopsis Iterative Methods for Solving Linear Systems by : Anne Greenbaum
Mathematics of Computing -- Numerical Analysis.
Author |
: David R. Kincaid |
Publisher |
: Academic Press |
Total Pages |
: 350 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483260204 |
ISBN-13 |
: 1483260208 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Iterative Methods for Large Linear Systems by : David R. Kincaid
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 |
: Gabriele Ciaramella |
Publisher |
: SIAM |
Total Pages |
: 285 |
Release |
: 2022-02-08 |
ISBN-10 |
: 9781611976908 |
ISBN-13 |
: 1611976901 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Iterative Methods and Preconditioners for Systems of Linear Equations by : Gabriele Ciaramella
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.