Direct Methods For Sparse Linear Systems
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Direct Methods For Sparse Linear Systems
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Author : Timothy A. Davis
language : en
Publisher: SIAM
Release Date : 2006-09-01
Direct Methods For Sparse Linear Systems written by Timothy A. Davis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-01 with Computers categories.
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.
Iterative Methods For Sparse Linear Systems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01
Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.
Mathematics of Computing -- General.
Direct Methods For Sparse Matrices
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Author : I. S. Duff
language : en
Publisher: Oxford University Press
Release Date : 2017-02-10
Direct Methods For Sparse Matrices written by I. S. Duff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-10 with Mathematics categories.
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.
Iterative Krylov Methods For Large Linear Systems
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Author : H. A. van der Vorst
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
Iterative Krylov Methods For Large Linear Systems written by H. A. van der Vorst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.
Sparse Matrix Technology
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Author : Sergio Pissanetzky
language : en
Publisher: Academic Press
Release Date : 2014-06-28
Sparse Matrix Technology written by Sergio Pissanetzky and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting.
Direct Methods For Sparse Matrices
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Author : O. Østerby
language : en
Publisher: Springer
Release Date : 1983
Direct Methods For Sparse Matrices written by O. Østerby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Iterative Methods For Large Linear Systems
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Author : David R. Kincaid
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Iterative Methods For Large Linear Systems written by David R. Kincaid and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Introduction To Parallel And Vector Solution Of Linear Systems
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Author : James M. Ortega
language : en
Publisher: Springer Science & Business Media
Release Date : 1988-04-30
Introduction To Parallel And Vector Solution Of Linear Systems written by James M. Ortega and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-30 with Computers categories.
Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
Parallel Numerical Algorithms
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Author : David E. Keyes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parallel Numerical Algorithms written by David E. Keyes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.