Krylov Subspace Methods
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Iterative Methods For Sparse Linear Systems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01
Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.
Mathematics of Computing -- General.
The Matrix Eigenvalue Problem
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Author : David S. Watkins
language : en
Publisher: SIAM
Release Date : 2007-01-01
The Matrix Eigenvalue Problem written by David S. Watkins and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
An in-depth, theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems.
Iterative Krylov Methods For Large Linear Systems
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Author : H. A. van der Vorst
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Iterative Krylov Methods For Large Linear Systems written by H. A. van der Vorst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Iterative Methods For Linear Systems
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Author : Maxim A. Olshanskii
language : en
Publisher: SIAM
Release Date : 2014-01-01
Iterative Methods For Linear Systems written by Maxim A. Olshanskii and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Mathematics categories.
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.
Numerical Methods For Large Eigenvalue Problems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2011-05-26
Numerical Methods For Large Eigenvalue Problems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
This revised edition discusses numerical methods for computing the 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.
Krylov Subspace Methods For Linear Systems
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Author : Tomohiro Sogabe
language : en
Publisher: Springer Nature
Release Date : 2023-01-20
Krylov Subspace Methods For Linear Systems written by Tomohiro Sogabe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.
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.
Krylov Subspace Methods With Application In Incompressible Fluid Flow Solvers
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Author : Iman Farahbakhsh
language : en
Publisher: John Wiley & Sons
Release Date : 2020-09-15
Krylov Subspace Methods With Application In Incompressible Fluid Flow Solvers written by Iman Farahbakhsh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-15 with Science categories.
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.
Trust Region Methods
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Author : A. R. Conn
language : en
Publisher: SIAM
Release Date : 2000-01-01
Trust Region Methods written by A. R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Mathematics of Computing -- General.
Convergence Of Iterations For Linear Equations
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Author : Olavi Nevanlinna
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Convergence Of Iterations For Linear Equations written by Olavi Nevanlinna and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
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.
Iterative Methods For Solving Linear Systems
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Author : Anne Greenbaum
language : en
Publisher: SIAM
Release Date : 1997-01-01
Iterative Methods For Solving Linear Systems written by Anne Greenbaum and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.