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Author : Anonim
Publisher : Springer-Verlag
Page : 283 pages
File Size : 53,7 Mb
Release : 2013-07-01
Category : Technology & Engineering
ISBN : 9783663111085
Author : Bernd Fischer
Publisher : SIAM
Page : 284 pages
File Size : 41,6 Mb
Release : 2011-07-28
Category : Mathematics
ISBN : 9781611971910
Originally published: Chichester; New York: Wiley; Stuttgart: Teubner, c1996.
Author : Dominique Orban,Mario Arioli
Publisher : SIAM
Page : 101 pages
File Size : 52,7 Mb
Release : 2017-04-07
Category : Mathematics
ISBN : 9781611974720
Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure. This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia. The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.
Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 244 pages
File Size : 42,7 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464
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 : Yousef Saad
Publisher : SIAM
Page : 546 pages
File Size : 44,5 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718007
Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
Author : Anne Greenbaum
Publisher : SIAM
Page : 225 pages
File Size : 45,8 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713961
Mathematics of Computing -- Numerical Analysis.
Author : Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
Publisher : SIAM
Page : 130 pages
File Size : 45,7 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 9780898713282
Mathematics of Computing -- Numerical Analysis.
Author : Are Magnus Bruaset
Publisher : Routledge
Page : 175 pages
File Size : 49,8 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469371
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 : David R. Kincaid,Linda J. Hayes
Publisher : Academic Press
Page : 350 pages
File Size : 50,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260204
Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.
Author : Dominique Orban,Mario Arioli
Publisher : SIAM
Page : 93 pages
File Size : 45,8 Mb
Release : 2017-04-07
Category : Mathematics
ISBN : 9781611974737
Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure.÷ This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia.÷ The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.÷
Author : Rizos Sakellariou,John Keane,John Gurd,Len Freeman
Publisher : Springer
Page : 950 pages
File Size : 48,6 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540446811
Euro-Par – the European Conference on Parallel Computing – is an international conference series dedicated to the promotion and advancement of all aspects of parallel computing. The major themes can be divided into the broad categories of hardware, software, algorithms, and applications for parallel computing. The objective of Euro-Par is to provide a forum within which to promote the dev- opment of parallel computing both as an industrial technique and an academic discipline, extending the frontiers of both the state of the art and the state of the practice. This is particularlyimportant at a time when parallel computing is undergoing strong and sustained development and experiencing real ind- trial take up. The main audience for and participants in Euro-Par are seen as researchers in academic departments, government laboratories, and industrial organisations. Euro-Par aims to become the primarychoice of such professionals for the presentation of new results in their speci?c areas. Euro-Par is also int- ested in applications that demonstrate the e?ectiveness of the main Euro-Par themes. Euro-Par has its own Internet domain with a permanent web site where the historyof the conference series is described: http://www. euro-par. org. The Euro-Par conference series is sponsored bythe Association of Computer Machineryand the International Federation of Information Processing. Euro-Par 2001 Euro-Par 2001 was organised bythe Universityof Manchester and UMIST.
Author : Robert E. O'Malley
Publisher : SIAM
Page : 424 pages
File Size : 43,7 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 0898713021
Proceedings -- Computer Arithmetic, Algebra, OOP.
Author : David M. Young
Publisher : Elsevier
Page : 598 pages
File Size : 41,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483274133
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.
Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 49,9 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908
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 : E. J. Hannan,Manfred Deistler
Publisher : SIAM
Page : 418 pages
File Size : 49,5 Mb
Release : 2012-05-31
Category : Business & Economics
ISBN : 9781611972184
Originally published: New York: Wiley, c1988.