Solving Linear Systems on Vector and Shared Memory Computers PDF Download
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Author: Jack J. Dongarra
Publisher:
ISBN:
Category :
Languages : en
Pages : 256
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Book Description
Author: Jack J. Dongarra
Publisher:
ISBN:
Category :
Languages : en
Pages : 256
Get Book Here
Book Description
Author: J. J. Dongarra
Publisher: Society for Industrial and Applied Mathematics (SIAM)
ISBN:
Category : Computers
Languages : en
Pages : 274
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Book Description
Mathematics of Computing -- Parallelism.
Author:
Publisher:
ISBN:
Category :
Languages : es
Pages : 256
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Book Description
Author: J. J. Dongarra
Publisher: Cambridge University Press
ISBN: 9780898714289
Category : Computers
Languages : en
Pages : 368
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Book Description
This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text.
Author: K. Gallivan
Publisher: SIAM
ISBN: 9781611971705
Category : Mathematics
Languages : en
Pages : 207
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Book Description
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.
Author: Gene H. Golub
Publisher: JHU Press
ISBN: 1421408597
Category : Mathematics
Languages : en
Pages : 781
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Book Description
A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.
Author: Gerard Meurant
Publisher: Elsevier
ISBN: 0080529518
Category : Mathematics
Languages : en
Pages : 777
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Book Description
This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Author: H. A. van der Vorst
Publisher: Cambridge University Press
ISBN: 9780521818285
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Table of contents
Author: Pi-Yu Chung
Publisher:
ISBN:
Category :
Languages : en
Pages : 146
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Book Description
This paper describes an efficient approach for solving sparse linear systems using direct method on a shared-memory vector multiprocessor computer. The direct method is divided into three steps: LU factorization, forward substitution and backward substitution. If the size of the linear system is large, LU factorization is a very time-consuming step, so that concurrency and vectorization are exploited to reduce execution time. Parallelism of LU factorization is obtained by partitioning the matrix using multilevel node-tearing techniques. The partitioned matrix is reordered into a NBBD (Nested Bordered-Block Diagonal) form. A nested-block data structure is used to store the sparse matrix, enabling the use of vectorization as well as multiprocessing to achieve high performance. This approach is suitable for many applications that require the repeated direct solution of sparse linear systems with identical matrix structure, such as circuit simulation. The approach has been implemented in a program that runs on an ALLIANT FX/8 vector multiprocessor with shared memory. Speedups in execution time compared to conventional serial computation with no vectorization are up to 20 using eight processors. Keywords: Sparse matrix, Parallel solution, Multi-processors vectorization, Linear systems, Nodes, Computers, Theses, Parallel orientation. (CP).
Author: Yves Robert
Publisher: Manchester University Press
ISBN: 9780719033650
Category : Algorithms
Languages : en
Pages : 216
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Book Description
Mathematics of Computing -- Parallelism.
