Polynomial Based Iteration Methods for Symmetric Linear Systems PDF Download
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Author:
Publisher: Springer-Verlag
ISBN: 3663111083
Category : Technology & Engineering
Languages : de
Pages : 282
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Book Description
Author:
Publisher: Springer-Verlag
ISBN: 3663111083
Category : Technology & Engineering
Languages : de
Pages : 282
Get Book Here
Book Description
Author: Bernd Fischer
Publisher: SIAM
ISBN: 1611971918
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Originally published: Chichester; New York: Wiley; Stuttgart: Teubner, c1996.
Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537
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Book Description
Mathematics of Computing -- General.
Author: Anne Greenbaum
Publisher: SIAM
ISBN: 9781611970937
Category : Mathematics
Languages : en
Pages : 235
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Book Description
Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study. Greenbaum includes important material on the effect of rounding errors on iterative methods that has not appeared in other books on this subject. Additional important topics include a discussion of the open problem of finding a provably near-optimal short recurrence for non-Hermitian linear systems; the relation of matrix properties such as the field of values and the pseudospectrum to the convergence rate of iterative methods; comparison theorems for preconditioners and discussion of optimal preconditioners of specified forms; introductory material on the analysis of incomplete Cholesky, multigrid, and domain decomposition preconditioners, using the diffusion equation and the neutron transport equation as example problems. A small set of recommended algorithms and implementations is included.
Author: H. A. van der Vorst
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Table of contents
Author: Louis A. Hageman
Publisher: Elsevier
ISBN: 1483294374
Category : Mathematics
Languages : en
Pages : 409
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Book Description
Applied Iterative Methods
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 0898713617
Category : Mathematics
Languages : en
Pages : 356
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Book Description
Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra.
Author: Lloyd N. Trefethen
Publisher: Princeton University Press
ISBN: 0691213100
Category : Mathematics
Languages : en
Pages : 626
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Book Description
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Author: Wolfgang Hackbusch
Publisher: Springer
ISBN: 3319284835
Category : Mathematics
Languages : en
Pages : 528
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Book Description
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Author: Zhong-Zhi Bai
Publisher: SIAM
ISBN: 1611976634
Category : Mathematics
Languages : en
Pages : 496
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Book Description
This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
