Iterative Methods For Linear Systems PDF Download
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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 | : 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 | : 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 | : C. T. Kelley |
Publisher | : SIAM |
Total Pages | : 179 |
Release | : 1995-01-01 |
Genre | : Mathematics |
ISBN | : 9781611970944 |
Download Iterative Methods for Linear and Nonlinear Equations Book in PDF, ePub and Kindle
Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.
Author | : Gabriele Ciaramella |
Publisher | : SIAM |
Total Pages | : 285 |
Release | : 2022-02-08 |
Genre | : Mathematics |
ISBN | : 1611976901 |
Download Iterative Methods and Preconditioners for Systems of Linear Equations Book in PDF, ePub and Kindle
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 | : Richard Barrett |
Publisher | : SIAM |
Total Pages | : 141 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9781611971538 |
Download Templates for the Solution of Linear Systems Book in PDF, ePub and Kindle
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.
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 | : Daniele Bertaccini |
Publisher | : CRC Press |
Total Pages | : 321 |
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 | : Louis A. Hageman |
Publisher | : Elsevier |
Total Pages | : 409 |
Release | : 2014-06-28 |
Genre | : Mathematics |
ISBN | : 1483294374 |
Download Applied Iterative Methods Book in PDF, ePub and Kindle
Applied Iterative Methods
Author | : David M. Young |
Publisher | : Elsevier |
Total Pages | : 599 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483274136 |
Download Iterative Solution of Large Linear Systems Book in PDF, ePub and Kindle
Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.