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Iterative Incomplete Factorization Methods

Author : Valeri? Pavlovich Il?in

Publisher : World Scientific

Page : 212 pages

File Size : 15,67 MB

Release : 1992

Category : Mathematics

ISBN : 9789810209964

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Book Description

This book is devoted to numerical methods for solving sparse linear algebra systems of very large dimension which arise in the implementation of the mesh approximations of the partial differential equations. Incomplete factorization is the basis of the wide class of preconditioning interative processes with acceleration by conjugate gradients or the Chebyshev technique. Different kinds of explicit and implicit algorithms are considered. Theoretical grounds of correctness and estimates of the convergence velocity of iterations are presented. Together with the results of experimental investigations for the typical examples, this book is the first on systematic studying of the incomplete factorization methods.





Parallel Numerical Algorithms

Author : David E. Keyes

Publisher : Springer Science & Business Media

Page : 403 pages

File Size : 43,9 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 9401154120

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Book Description

In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.



Iterative Solution Methods

Author : Owe Axelsson

Publisher : Cambridge University Press

Page : 676 pages

File Size : 12,87 MB

Release : 1996-03-29

Category : Mathematics

ISBN : 9780521555692

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Book Description

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.



A Survey of Preconditioned Iterative Methods

Author : Are Magnus Bruaset

Publisher : Routledge

Page : 175 pages

File Size : 48,91 MB

Release : 2018-12-13

Category : Mathematics

ISBN : 1351469371

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Book Description

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



Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications

Author : Daniele Bertaccini

Publisher : CRC Press

Page : 321 pages

File Size : 10,58 MB

Release : 2018-02-19

Category : Mathematics

ISBN : 1351649612

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Book Description

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.



Iterative Methods for Sparse Linear Systems

Author : Yousef Saad

Publisher : SIAM

Page : 546 pages

File Size : 14,51 MB

Release : 2003-01-01

Category : Mathematics

ISBN : 9780898718003

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Book Description

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.



Computer Algorithms for Solving Linear Algebraic Equations

Author : Emilio Spedicato

Publisher : Springer Science & Business Media

Page : 361 pages

File Size : 35,80 MB

Release : 2012-12-06

Category : Computers

ISBN : 3642767176

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Book Description

The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.



Iterative Methods for Large Linear Systems

Author : David R. Kincaid

Publisher : Academic Press

Page : 350 pages

File Size : 25,72 MB

Release : 2014-05-10

Category : Mathematics

ISBN : 1483260208

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Book Description

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.



Encyclopedia of Parallel Computing

Author : David Padua

Publisher : Springer Science & Business Media

Page : 2211 pages

File Size : 27,75 MB

Release : 2014-07-08

Category : Computers

ISBN : 038709766X

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Book Description

Containing over 300 entries in an A-Z format, the Encyclopedia of Parallel Computing provides easy, intuitive access to relevant information for professionals and researchers seeking access to any aspect within the broad field of parallel computing. Topics for this comprehensive reference were selected, written, and peer-reviewed by an international pool of distinguished researchers in the field. The Encyclopedia is broad in scope, covering machine organization, programming languages, algorithms, and applications. Within each area, concepts, designs, and specific implementations are presented. The highly-structured essays in this work comprise synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searchers for immediate access to useful information. Key concepts presented in the Encyclopedia of Parallel Computing include; laws and metrics; specific numerical and non-numerical algorithms; asynchronous algorithms; libraries of subroutines; benchmark suites; applications; sequential consistency and cache coherency; machine classes such as clusters, shared-memory multiprocessors, special-purpose machines and dataflow machines; specific machines such as Cray supercomputers, IBM’s cell processor and Intel’s multicore machines; race detection and auto parallelization; parallel programming languages, synchronization primitives, collective operations, message passing libraries, checkpointing, and operating systems. Topics covered: Speedup, Efficiency, Isoefficiency, Redundancy, Amdahls law, Computer Architecture Concepts, Parallel Machine Designs, Benmarks, Parallel Programming concepts & design, Algorithms, Parallel applications. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references and to additional significant research. Related Subjects: supercomputing, high-performance computing, distributed computing