Parallel Distributed Direct Method For Solving Linear Systems
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| Author | : Timothy A. Davis |
| Publisher | : SIAM |
| Total Pages | : 228 |
| Release | : 2006-09-01 |
| Genre | : Computers |
| ISBN | : 0898716136 |
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 |
| Total Pages | : 451 |
| Release | : 2017-03-09 |
| Genre | : Mathematics |
| ISBN | : 0192507508 |
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 | : Dimitri Bertsekas |
| Publisher | : Athena Scientific |
| Total Pages | : 832 |
| Release | : 2015-03-01 |
| Genre | : Mathematics |
| ISBN | : 1886529159 |
This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.
| Author | : Stefan Mayer |
| Publisher | : Herbert Utz Verlag |
| Total Pages | : 224 |
| Release | : 1998 |
| Genre | : |
| ISBN | : 9783896753861 |
| Author | : Timothy A. Davis |
| Publisher | : SIAM |
| Total Pages | : 229 |
| Release | : 2006-01-01 |
| Genre | : Computers |
| ISBN | : 9780898718881 |
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.
| Author | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 537 |
| Release | : 2003-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898715342 |
Mathematics of Computing -- General.
| Author | : |
| Publisher | : |
| Total Pages | : 704 |
| Release | : 1995 |
| Genre | : Aeronautics |
| ISBN | : |
| Author | : Richard Barrett |
| Publisher | : SIAM |
| Total Pages | : 141 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971538 |
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 | : Christian Lengauer |
| Publisher | : Springer |
| Total Pages | : 1382 |
| Release | : 2005-11-23 |
| Genre | : Computers |
| ISBN | : 3540695494 |
This book constitutes the refereed proceedings of the Third International Euro-Par Conference, held in Passau, Germany, in August 1997. The 178 revised papers presented were selected from more than 300 submissions on the basis of 1101 reviews. The papers are organized in accordance with the conference workshop structure in tracks on support tools and environments, routing and communication, automatic parallelization, parallel and distributed algorithms, programming languages, programming models and methods, numerical algorithms, parallel architectures, HPC applications, scheduling and load balancing, performance evaluation, instruction-level parallelism, database systems, symbolic computation, real-time systems, and an ESPRIT workshop.
| Author | : Michael A. Heroux |
| Publisher | : SIAM |
| Total Pages | : 407 |
| Release | : 2006-01-01 |
| Genre | : Computers |
| ISBN | : 0898716195 |
Scientific computing has often been called the third approach to scientific discovery, emerging as a peer to experimentation and theory. Historically, the synergy between experimentation and theory has been well understood: experiments give insight into possible theories, theories inspire experiments, experiments reinforce or invalidate theories, and so on. As scientific computing has evolved to produce results that meet or exceed the quality of experimental and theoretical results, it has become indispensable.Parallel processing has been an enabling technology in scientific computing for more than 20 years. This book is the first in-depth discussion of parallel computing in 10 years; it reflects the mix of topics that mathematicians, computer scientists, and computational scientists focus on to make parallel processing effective for scientific problems. Presently, the impact of parallel processing on scientific computing varies greatly across disciplines, but it plays a vital role in most problem domains and is absolutely essential in many of them. Parallel Processing for Scientific Computing is divided into four parts: The first concerns performance modeling, analysis, and optimization; the second focuses on parallel algorithms and software for an array of problems common to many modeling and simulation applications; the third emphasizes tools and environments that can ease and enhance the process of application development; and the fourth provides a sampling of applications that require parallel computing for scaling to solve larger and realistic models that can advance science and engineering. This edited volume serves as an up-to-date reference for researchers and application developers on the state of the art in scientific computing. It also serves as an excellent overview and introduction, especially for graduate and senior-level undergraduate students interested in computational modeling and simulation and related computer science and applied mathematics aspects.Contents List of Figures; List of Tables; Preface; Chapter 1: Frontiers of Scientific Computing: An Overview; Part I: Performance Modeling, Analysis and Optimization. Chapter 2: Performance Analysis: From Art to Science; Chapter 3: Approaches to Architecture-Aware Parallel Scientific Computation; Chapter 4: Achieving High Performance on the BlueGene/L Supercomputer; Chapter 5: Performance Evaluation and Modeling of Ultra-Scale Systems; Part II: Parallel Algorithms and Enabling Technologies. Chapter 6: Partitioning and Load Balancing; Chapter 7: Combinatorial Parallel and Scientific Computing; Chapter 8: Parallel Adaptive Mesh Refinement; Chapter 9: Parallel Sparse Solvers, Preconditioners, and Their Applications; Chapter 10: A Survey of Parallelization Techniques for Multigrid Solvers; Chapter 11: Fault Tolerance in Large-Scale Scientific Computing; Part III: Tools and Frameworks for Parallel Applications. Chapter 12: Parallel Tools and Environments: A Survey; Chapter 13: Parallel Linear Algebra Software; Chapter 14: High-Performance Component Software Systems; Chapter 15: Integrating Component-Based Scientific Computing Software; Part IV: Applications of Parallel Computing. Chapter 16: Parallel Algorithms for PDE-Constrained Optimization; Chapter 17: Massively Parallel Mixed-Integer Programming; Chapter 18: Parallel Methods and Software for Multicomponent Simulations; Chapter 19: Parallel Computational Biology; Chapter 20: Opportunities and Challenges for Parallel Computing in Science and Engineering; Index.
