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Krylov Subspace Methods For Linear Systems
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Book Synopsis Krylov Subspace Methods by : Jörg Liesen
Download or read book Krylov Subspace Methods written by Jörg Liesen and published by Numerical Mathematics and Scie. This book was released on 2013 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Iterative Krylov Methods for Large Linear Systems by : H. A. van der Vorst
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Iterative Methods for Linear Systems by : Maxim A. Olshanskii
Download or read book Iterative Methods for Linear Systems written by Maxim A. Olshanskii and published by SIAM. This book was released on 2014-07-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.??
Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Book Synopsis Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers by : Iman Farahbakhsh
Download or read book Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers written by Iman Farahbakhsh and published by John Wiley & Sons. This book was released on 2020-09-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: A succinct and complete explanation of Krylov subspace methods for solving systems of equations Krylov Subspace Methods with Application in Incompressible Fluid Flow Solvers is the most current and complete guide to the implementation of Krylov subspace methods for solving systems of equations with different types of matrices. Written in the simplest language possible and eliminating ambiguities, the text is easy to follow for post-grad students and applied mathematicians alike. The book covers a breadth of topics, including: The different methods used in solving the systems of equations with ill-conditioned and well-conditioned matrices The behavior of Krylov subspace methods in the solution of systems with ill-posed singular matrices Expertly supported with the addition of a companion website hosting computer programs of appendices The book includes executable subroutines and main programs that can be applied in CFD codes as well as appendices that support the results provided throughout the text. There is no other comparable resource to prepare the reader to use Krylov subspace methods in incompressible fluid flow solvers.
Book Synopsis Krylov Subspace Methods for Linear Systems by : Tomohiro Sogabe
Download or read book Krylov Subspace Methods for Linear Systems written by Tomohiro Sogabe and published by Springer Nature. This book was released on 2023-01-20 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems. The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view. The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.
Book Synopsis Iterative Methods for Solving Linear Systems by : Anne Greenbaum
Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Book Synopsis Convergence of Iterations for Linear Equations by : Olavi Nevanlinna
Download or read book Convergence of Iterations for Linear Equations written by Olavi Nevanlinna and published by Birkhäuser. This book was released on 2012-12-06 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem.
Book Synopsis The Matrix Eigenvalue Problem by : David S. Watkins
Download or read book The Matrix Eigenvalue Problem written by David S. Watkins and published by SIAM. This book was released on 2007-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
Book Synopsis Solving Nonlinear Equations with Newton's Method by : C. T. Kelley
Download or read book Solving Nonlinear Equations with Newton's Method written by C. T. Kelley and published by SIAM. This book was released on 2003-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Numerical Methods for Large Eigenvalue Problems by : Yousef Saad
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Book Synopsis Iterative Methods for Linear and Nonlinear Equations by : C. T. Kelley
Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley and published by SIAM. This book was released on 1995-01-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Templates for the Solution of Linear Systems by : Richard Barrett
Download or read book Templates for the Solution of Linear Systems written by Richard Barrett and published by SIAM. This book was released on 1994-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Linear Algebra and Applications by : Biswa Nath Datta
Download or read book Numerical Linear Algebra and Applications written by Biswa Nath Datta and published by SIAM. This book was released on 2010-01-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.
Book Synopsis Iterative Solution of Large Linear Systems by : David M. Young
Download or read book Iterative Solution of Large Linear Systems written by David M. Young and published by Elsevier. This book was released on 2014-05-10 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computer Solution of Large Linear Systems by : Gerard Meurant
Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
