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An Efficient Parallel Algorithm For The Solution Of A Tridiagonal Linear System Of Equations
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Book Synopsis An efficient parallel algorithm for the solution of a tridiagonal linear system of equations by : Harold S. Stone
Download or read book An efficient parallel algorithm for the solution of a tridiagonal linear system of equations written by Harold S. Stone and published by . This book was released on 1971 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tridiagonal linear systems of equations can be solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computation on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log of N to the base 2. The algorithm is based on recursive relations, and can be used to solve recurrence relations of all orders. (Author).
Book Synopsis Analysis of a Parallel Algorithm for the Solution of a Linear Tridiagonal System of Equations by : Praveen N. Moudgal
Download or read book Analysis of a Parallel Algorithm for the Solution of a Linear Tridiagonal System of Equations written by Praveen N. Moudgal and published by . This book was released on 1987 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algorithms for Elliptic Problems by : Marián Vajtersic
Download or read book Algorithms for Elliptic Problems written by Marián Vajtersic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.
Book Synopsis New Parallel Algorithms for Direct Solution of Linear Equations by : C. Siva Ram Murthy
Download or read book New Parallel Algorithms for Direct Solution of Linear Equations written by C. Siva Ram Murthy and published by Wiley-Interscience. This book was released on 2000-10-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Parallel Algorithms for Optimal Control of Large Scale Linear Systems by : Zoran Gajic
Download or read book Parallel Algorithms for Optimal Control of Large Scale Linear Systems written by Zoran Gajic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel Algorithms for Optimal Control of Large Scale Linear Systems is a comprehensive presentation for both linear and bilinear systems. The parallel algorithms presented in this book are applicable to a wider class of practical systems than those served by traditional methods for large scale singularly perturbed and weakly coupled systems based on the power-series expansion methods. It is intended for scientists and advance graduate students in electrical engineering and computer science who deal with parallel algorithms and control systems, especially large scale systems. The material presented is both comprehensive and unique.
Book Synopsis Parallel Algorithms for Numerical Linear Algebra by : H. van der Vorst
Download or read book Parallel Algorithms for Numerical Linear Algebra written by H. van der Vorst and published by Elsevier. This book was released on 2014-06-28 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for parallel shared-memory systems, and the design of fast algorithms and implementations for vector supercomputers.
Book Synopsis Divide and Conquer by : Stefan Bondeli
Download or read book Divide and Conquer written by Stefan Bondeli and published by . This book was released on 1990 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Parallel and Vector Solution of Linear Systems by : James M. Ortega
Download or read book Introduction to Parallel and Vector Solution of Linear Systems written by James M. Ortega and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parallel Algorithms for Matrix Computations by : K. Gallivan
Download or read book Parallel Algorithms for Matrix Computations written by K. Gallivan and published by SIAM. This book was released on 1990-01-01 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book NASA Technical Paper written by and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Efficient Parallel Solution of Linear Systems by : Victor Pan
Download or read book Efficient Parallel Solution of Linear Systems written by Victor Pan and published by . This book was released on 1985* with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most efficient known parallel algorithms for inversion of a nonsingular nxn matrix A or solving a linear system Ax=b over the rationals require O(log n) to the 2nd power time and M(n) square root of n processors (where M(n) is the number of processors required in order to multiply two nxn rational matrices in time O(log n)). Furthermore, all known polylog time algorithms for those problems are unstable: they require the calculations to be done with perfect precision; otherwise they give no results at all. This paper describes parallel algorithms that have good numerical stability and remain efficient as n grows large. Additional keywords: Iterations; Convergence; Newtons method; Computer architecture.
Book Synopsis A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations by : Peter M. Kogge
Download or read book A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations written by Peter M. Kogge and published by . This book was released on 1972 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parallel Complexity Of Linear System Solution by : Bruno Codenotti
Download or read book Parallel Complexity Of Linear System Solution written by Bruno Codenotti and published by World Scientific. This book was released on 1991-04-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important parallel algorithms for the solution of linear systems. Despite the evolution and significance of the field of parallel solution of linear systems, no book is completely dedicated to the subject. People interested in the themes covered by this book belong to two different groups: numerical linear algebra and theoretical computer science, and this is the first effort to produce a useful tool for both. The book is organized as follows: after introducing the general features of parallel algorithms and the most important models of parallel computation, the authors analyze the complexity of solving linear systems in the circuit, PRAM, distributed, and VLSI models. The approach covers both the general case (i.e. dense linear systems without structure) and many important special cases (i.e. banded, sparse, Toeplitz, circulant linear systems).
Book Synopsis Introduction to Parallel Algorithms by : C. Xavier
Download or read book Introduction to Parallel Algorithms written by C. Xavier and published by John Wiley & Sons. This book was released on 1998-08-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel algorithms Made Easy The complexity of today's applications coupled with the widespread use of parallel computing has made the design and analysis of parallel algorithms topics of growing interest. This volume fills a need in the field for an introductory treatment of parallel algorithms-appropriate even at the undergraduate level, where no other textbooks on the subject exist. It features a systematic approach to the latest design techniques, providing analysis and implementation details for each parallel algorithm described in the book. Introduction to Parallel Algorithms covers foundations of parallel computing; parallel algorithms for trees and graphs; parallel algorithms for sorting, searching, and merging; and numerical algorithms. This remarkable book: * Presents basic concepts in clear and simple terms * Incorporates numerous examples to enhance students' understanding * Shows how to develop parallel algorithms for all classical problems in computer science, mathematics, and engineering * Employs extensive illustrations of new design techniques * Discusses parallel algorithms in the context of PRAM model * Includes end-of-chapter exercises and detailed references on parallel computing. This book enables universities to offer parallel algorithm courses at the senior undergraduate level in computer science and engineering. It is also an invaluable text/reference for graduate students, scientists, and engineers in computer science, mathematics, and engineering.
Book Synopsis Applied Parallel and Scientific Computing by : Pekka Manninen
Download or read book Applied Parallel and Scientific Computing written by Pekka Manninen and published by Springer. This book was released on 2013-02-12 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the refereed proceedings of the 11th International Conference on Applied Parallel and Scientific Computing, PARA 2012, held in Helsinki, Finland, in June 2012. The 35 revised full papers presented were selected from numerous submissions and are organized in five technical sessions covering the topics of advances in HPC applications, parallel algorithms, performance analyses and optimization, application of parallel computing in industry and engineering, and HPC interval methods. In addition, three of the topical minisymposia are described by a corresponding overview article on the minisymposia topic. In order to cover the state-of-the-art of the field, at the end of the book a set of abstracts describe some of the conference talks not elaborated into full articles.
Download or read book NASA Technical Note written by and published by . This book was released on 1974 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High Performance Algorithms for Structured Matrix Problems by : Peter Arbenz
Download or read book High Performance Algorithms for Structured Matrix Problems written by Peter Arbenz and published by Nova Publishers. This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises 10 contributions that summarize the state of the art in the areas of high performance solutions of structured linear systems and structured eigenvalue and singular-value problems. Topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. Specific paper topics include: the stable parallel solution of general narrow banded linear systems; efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form; a numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems; and parallel CG-methods automatically optimized for PC and workstation clusters. Annotation copyrighted by Book News, Inc., Portland, OR
