Iterative Solution Of Symmetric Quasi Definite Linear Systems

Author : Dominique Orban,Mario Arioli
Publisher : SIAM
Page : 93 pages
File Size : 45,5 Mb
Release : 2017-04-07
Category : Mathematics
ISBN : 9781611974737

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Iterative Solution of Symmetric Quasi-definite Linear Systems by Dominique Orban,Mario Arioli Pdf

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 : David M. Young
Publisher : Elsevier
Page : 598 pages
File Size : 52,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483274133

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Iterative Solution of Large Linear Systems by David M. Young Pdf

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 : 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 : 141 pages
File Size : 50,6 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611971535

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Templates for the Solution of Linear Systems by Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst Pdf

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.

Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Page : 285 pages
File Size : 47,7 Mb
Release : 2022-02-08
Category : Mathematics
ISBN : 9781611976908

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Iterative Methods and Preconditioners for Systems of Linear Equations by Gabriele Ciaramella,Martin J. Gander Pdf

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 : Anne Greenbaum
Publisher : SIAM
Page : 225 pages
File Size : 44,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713961

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Iterative Methods for Solving Linear Systems by Anne Greenbaum Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
Publisher : SIAM
Page : 244 pages
File Size : 43,6 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781611973464

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Iterative Methods for Linear Systems by Maxim A. Olshanskii,Eugene E. Tyrtyshnikov Pdf

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 : 537 pages
File Size : 42,6 Mb
Release : 2003-04-01
Category : Mathematics
ISBN : 9780898715347

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

Mathematics of Computing -- General.

Author : David R. Kincaid,Linda J. Hayes
Publisher : Academic Press
Page : 350 pages
File Size : 42,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260204

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Iterative Methods for Large Linear Systems by David R. Kincaid,Linda J. Hayes Pdf

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 : Anonim
Publisher : Springer-Verlag
Page : 283 pages
File Size : 49,6 Mb
Release : 2013-07-01
Category : Technology & Engineering
ISBN : 9783663111085

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Polynomial Based Iteration Methods for Symmetric Linear Systems by Anonim Pdf

Author : Yousef Saad
Publisher : SIAM
Page : 546 pages
File Size : 48,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718007

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Iterative Methods for Sparse Linear Systems by Yousef Saad Pdf

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 : J. M. Ortega,W. C. Rheinboldt
Publisher : Elsevier
Page : 592 pages
File Size : 50,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483276724

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Iterative Solution of Nonlinear Equations in Several Variables by J. M. Ortega,W. C. Rheinboldt Pdf

Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.

Author : Are Magnus Bruaset
Publisher : Routledge
Page : 175 pages
File Size : 47,8 Mb
Release : 2018-12-13
Category : Mathematics
ISBN : 9781351469371

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A Survey of Preconditioned Iterative Methods by Are Magnus Bruaset Pdf

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 : C. T. Kelley
Publisher : SIAM
Page : 169 pages
File Size : 49,9 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 9780898713527

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Daniele Bertaccini,Fabio Durastante
Publisher : CRC Press
Page : 366 pages
File Size : 55,8 Mb
Release : 2018-02-19
Category : Mathematics
ISBN : 9781351649612

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Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by Daniele Bertaccini,Fabio Durastante Pdf

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.

Author : Miroslav Rozložník
Publisher : Springer
Page : 136 pages
File Size : 43,9 Mb
Release : 2018-11-19
Category : Mathematics
ISBN : 9783030014315

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Saddle-Point Problems and Their Iterative Solution by Miroslav Rozložník Pdf

This book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering. The focus is on discussing the particular properties of such linear systems, and a large selection of algebraic methods for solving them, with an emphasis on iterative methods and preconditioning. The theoretical results presented here are complemented by a case study on potential fluid flow problem in a real world-application. This book is mainly intended for students of applied mathematics and scientific computing, but also of interest for researchers and engineers working on various applications. It is assumed that the reader has completed a basic course on linear algebra and numerical mathematics.