Krylov Methods For Nonsymmetric Linear Systems
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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with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms.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 | : H. A. van der Vorst |
Publisher | : Cambridge University Press |
Total Pages | : 242 |
Release | : 2003-04-17 |
Genre | : Mathematics |
ISBN | : 9780521818285 |
Download Iterative Krylov Methods for Large Linear Systems Book in PDF, Epub and Kindle
Table of contents
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 | : J. J. Dongarra |
Publisher | : Society for Industrial and Applied Mathematics (SIAM) |
Total Pages | : 274 |
Release | : 1991 |
Genre | : Computers |
ISBN | : |
Download Solving Linear Systems on Vector and Shared Memory Computers Book in PDF, Epub and Kindle
Mathematics of Computing -- Parallelism.
Author | : David E. Keyes |
Publisher | : Springer Science & Business Media |
Total Pages | : 403 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401154120 |
Download Parallel Numerical Algorithms Book in PDF, Epub and Kindle
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.
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 | : Are Magnus Bruaset |
Publisher | : Routledge |
Total Pages | : 175 |
Release | : 2018-12-13 |
Genre | : Mathematics |
ISBN | : 1351469371 |
Download A Survey of Preconditioned Iterative Methods Book in PDF, Epub and Kindle
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 | : Jörg Liesen |
Publisher | : Numerical Mathematics and Scie |
Total Pages | : 408 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 0199655413 |
Download Krylov Subspace Methods Book in PDF, Epub and Kindle
Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.
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.
Author | : David Ronald Kincaid |
Publisher | : |
Total Pages | : 360 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Iterative Methods for Large Linear Systems Book in PDF, Epub and Kindle
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