New Parallel Algorithms for Direct Solution of Linear Equations
New Parallel Algorithms for Direct Solution of Linear Equations

Author: C. Siva Ram Murthy

Publisher: Wiley-Interscience

Published: 2000-10-30

Total Pages: 192

ISBN-13:

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"Rather than parallelizing sequential algorithms, the authors develop new back-substitution free parallel algorithms, using a bidirectional elimination technique for the solution of both dense and sparse linear equations. They provide full coverage of bidirectional parallel algorithms based on Gaussian elimination, LU factorization, Householder reductions and modified Gram-Schmidt orthogonalization, Givens rotations, sparse Cholesky factorization, and sparse factorization, clearly demonstrating how the bidirectional approach allows for improved speedup, numerical stability, and efficient implementation on multiprocessor systems." "Plus, the book offers a useful survey of the vast literature on direct methods, introductory material on solving systems of linear equations, and exercises. It is an invaluable resource for computer scientists, researchers in parallel linear algebra, and anyone with an interest in parallel programming."--BOOK JACKET.

Parallel and Distributed Computation: Numerical Methods
Parallel and Distributed Computation: Numerical Methods

Author: Dimitri Bertsekas

Publisher: Athena Scientific

Published: 2015-03-01

Total Pages: 832

ISBN-13: 1886529159

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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.

Direct Methods for Sparse Linear Systems
Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

Published: 2006-09-01

Total Pages: 228

ISBN-13: 0898716136

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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.

Parallel Algorithms for Matrix Computations
Parallel Algorithms for Matrix Computations

Author: K. Gallivan

Publisher: SIAM

Published: 1990-01-01

Total Pages: 207

ISBN-13: 9781611971705

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Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.

Introduction to Parallel and Vector Solution of Linear Systems
Introduction to Parallel and Vector Solution of Linear Systems

Author: James M. Ortega

Publisher: Springer Science & Business Media

Published: 1988-04-30

Total Pages: 330

ISBN-13: 9780306428623

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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.

CONPAR 90 - VAPP IV
CONPAR 90 - VAPP IV

Author: Helmar Burkhart

Publisher: Springer Science & Business Media

Published: 1990-08-30

Total Pages: 936

ISBN-13: 9783540530657

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Parallel architectures are no longer pure research vehicles, as they were some years ago. There are now many commercial systems competing for market segments in scientific computing. The 1990s are likely to become the decade of parallel processing. CONPAR 90 - VAPP IV is the joint successor meeting of two highly successful international conference series in the field of vector and parallel processing. This volume contains the 79 papers presented at the conference. The various topics of the papers include hardware, software and application issues. Some of the session titles best reflect the contents: new models of computation, logic programming, large-grain data flow, interconnection networks, communication issues, reconfigurable and scalable systems, novel architectures and languages, high performance systems and accelerators, performance prediction / analysis / measurement, performance monitoring and debugging, compile-time analysis and restructurers, load balancing, process partitioning and concurrency control, visualization and runtime analysis, parallel linear algebra, architectures for image processing, efficient use of vector computers, transputer tools and applications, array processors, algorithmic studies for hypercube-type systems, systolic arrays and algorithms. The volume gives a comprehensive view of the state of the art in a field of current interest.

Introduction to Parallel and Vector Solution of Linear Systems
Introduction to Parallel and Vector Solution of Linear Systems

Author: James M. Ortega

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 309

ISBN-13: 1489921125

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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.