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Author : Jingyu Liu
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (56 download)
Download or read book Implementation of Block Iterative Methods for Non-symmetric Indefinite Linear Systems written by Jingyu Liu and published by . This book was released on 2002 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Barrett
Publisher : SIAM
ISBN 13 : 9781611971538
Total Pages : 141 pages
Book Rating : 4.9/5 (715 download)
Download or read book Templates for the Solution of Linear Systems written by Richard Barrett and published by SIAM. This book was released on 1994-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Author : Dominique Orban
Publisher : SIAM
ISBN 13 : 1611974739
Total Pages : 101 pages
Book Rating : 4.6/5 (119 download)
Download or read book Iterative Solution of Symmetric Quasi-definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Are Magnus Bruaset
Publisher : CRC Press
ISBN 13 : 9780582276543
Total Pages : 180 pages
Book Rating : 4.2/5 (765 download)
Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by CRC Press. This book was released on 1995-05-05 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 well suited for the kind of systems arising from the discretization of partial differential equations. The focus of this presentation is on the family of Krylov subspace solvers, of which the Conjugate Gradient algorithm is a typical example. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. When solving linear systems by iteration, a preconditioner is usually introduced in order to speed up convergence. In many cases, the selection of a proper preconditioner is crucial to the resulting computational performance. For this reason, this book pays special attention to different preconditioning strategies. Although aimed at a wide audience, the presentation assumes that the reader has basic knowledge of linear algebra, and to some extent, of partial differential equations. The comprehensive bibliography in this survey is provides an entry point to the enormous amount of published research in the field of iterative methods.
Author : Daniele Bertaccini
Publisher : CRC Press
ISBN 13 : 1351649612
Total Pages : 321 pages
Book Rating : 4.3/5 (516 download)
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : David Ronald Kincaid
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.:/5 (44 download)
Download or read book Iterative Methods for Large Linear Systems written by David Ronald Kincaid and published by . This book was released on 1990 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Author :
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (317 download)
Download or read book An Iterative Method for Indefinite Systems of Linear Equations written by and published by . This book was released on 1984 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.F/5 ( download)
Download or read book Preconditioners for Indefinite Systems Arising in Optimization written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1990 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We discuss the solution of sparse linear equations Ky = z, where K is symmetric and indefinite. Since exact solutions are not always required, direct and iterative methods are both of interest. An important direct method is the Bunch-Parlett factorization K = U sub T DU, where U is triangular and D is block-diagonal. A sparse implementation exists in the form of the Harwell code MA27. An appropriate iterative method is the conjugate-gradient-like algorithm SYMMLQ, which solves indefinite systems with the aid of a positive-definite preconditioner. For any indefinite matrix K, we show that the U sub T DU factorization can be modified at nominal cost to provide an exact preconditioner for SYMMLQ. We give code for overwriting the block-diagonal matrix D produced by MA27. We then study the KKT systems arising in barrier methods for linear and nonlinear programming, and derive preconditioners for use with SYMMLQ. For nonlinear programs we suggest a preconditioner based on the smaller KKT system associated with variables that are not near a bound. For linear programs we propose several preconditioners based on a square nonsingular matrix B that is analogous to the basis matrix in the simplex method. The aim is to facilitate solution of full KKT systems rather than equations of the form AD squared A sub T sub delta pi = r when the latter become excessively ill-conditioned. (kr).
Author : Gérard Meurant
Publisher : Springer Nature
ISBN 13 : 3030552519
Total Pages : 686 pages
Book Rating : 4.0/5 (35 download)
Download or read book Krylov Methods for Nonsymmetric Linear Systems written by Gérard Meurant and published by Springer Nature. This book was released on 2020-10-02 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.
Author : H. A. van der Vorst
Publisher : Cambridge University Press
ISBN 13 : 9780521818285
Total Pages : 242 pages
Book Rating : 4.8/5 (182 download)
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Author : Jennifer Scott
Publisher : Springer Nature
ISBN 13 : 3031258207
Total Pages : 254 pages
Book Rating : 4.0/5 (312 download)
Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.
Author : Anne Greenbaum
Publisher : SIAM
ISBN 13 : 089871396X
Total Pages : 225 pages
Book Rating : 4.8/5 (987 download)
Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Author : Timothy A. Davis
Publisher : SIAM
ISBN 13 : 0898716136
Total Pages : 228 pages
Book Rating : 4.8/5 (987 download)
Download or read book Direct Methods for Sparse Linear Systems written by Timothy A. Davis and published by SIAM. This book was released on 2006-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
Author : I. S. Duff
Publisher : Oxford University Press
ISBN 13 : 0192507516
Total Pages : 539 pages
Book Rating : 4.1/5 (925 download)
Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
Author : Roland W. Freund
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (833 download)
Download or read book Iterative Methods and Preconditioners for Nonsymmetric Linear Systems written by Roland W. Freund and published by . This book was released on 1994 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. David Brown
Publisher : SIAM
ISBN 13 : 9780898713398
Total Pages : 722 pages
Book Rating : 4.7/5 (133 download)
Download or read book Proceedings of the Cornelius Lanczos International Centenary Conference written by J. David Brown and published by SIAM. This book was released on 1994-01-01 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt:
