Iterative Krylov Methods For Large Linear Systems
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Author | : H. A. van der Vorst |
Publisher | : Cambridge University Press |
Total Pages | : 242 |
Release | : 2003-04-17 |
Genre | : Mathematics |
ISBN | : 9780521818285 |
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Table of contents
Author | : Henk A. van der Vorst |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2009-10-01 |
Genre | : Mathematics |
ISBN | : 9780521183703 |
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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 | : |
Total Pages | : 0 |
Release | : 2003 |
Genre | : |
ISBN | : |
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Author | : Yousef Saad |
Publisher | : SIAM |
Total Pages | : 537 |
Release | : 2003-04-01 |
Genre | : Mathematics |
ISBN | : 0898715342 |
Download Iterative Methods for Sparse Linear Systems Book in PDF, Epub and Kindle
Mathematics of Computing -- General.
Author | : Gérard Meurant |
Publisher | : Springer Nature |
Total Pages | : 686 |
Release | : 2020-10-02 |
Genre | : Mathematics |
ISBN | : 3030552519 |
Download Krylov Methods for Nonsymmetric Linear Systems Book in PDF, Epub and Kindle
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 |
Publisher | : Academic Press |
Total Pages | : 350 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483260208 |
Download Iterative Methods for Large Linear Systems Book in PDF, Epub and Kindle
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 | : Maxim A. Olshanskii |
Publisher | : SIAM |
Total Pages | : 257 |
Release | : 2014-07-21 |
Genre | : Mathematics |
ISBN | : 1611973465 |
Download Iterative Methods for Linear Systems Book in PDF, Epub and Kindle
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 | : Daniele Bertaccini |
Publisher | : CRC Press |
Total Pages | : 366 |
Release | : 2018-02-19 |
Genre | : Mathematics |
ISBN | : 1351649612 |
Download Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications Book in PDF, Epub and Kindle
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 | : Anne Greenbaum |
Publisher | : SIAM |
Total Pages | : 225 |
Release | : 1997-01-01 |
Genre | : Mathematics |
ISBN | : 089871396X |
Download Iterative Methods for Solving Linear Systems Book in PDF, Epub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Gerard Meurant |
Publisher | : Elsevier |
Total Pages | : 777 |
Release | : 1999-06-16 |
Genre | : Mathematics |
ISBN | : 0080529518 |
Download Computer Solution of Large Linear Systems Book in PDF, Epub and Kindle
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.