Efficient Algorithms for the Parallel Gaussian Elimination on Distributed Memory Machines PDF Download

Author: Abdel Krim Amoura
Publisher:
ISBN:
Category : Directed graphs
Languages : en
Pages : 18

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Author: Yves Robert
Publisher: Manchester University Press
ISBN: 9780719033650
Category : Computers
Languages : en
Pages : 216

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Book Description
Mathematics of Computing -- Parallelism.

Author: K. Gallivan
Publisher: SIAM
ISBN: 0898712602
Category : Mathematics
Languages : en
Pages : 204

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Book Description
Mathematics of Computing -- Parallelism.

Author: Xiaoye S. Li
Publisher:
ISBN:
Category : Decomposition (Mathematics)
Languages : en
Pages : 350

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Book Description
Abstract: "This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance computers, using Gaussian elimination with partial pivoting. The efficiencies of the new algorithms are demonstrated for matrices from various fields and for a variety of high performance machines. In the first part we discuss optimizations of a sequential algorithm to exploit the memory hierarchies that exist in most RISC-based superscalar computers. We begin with the left-looking supernode-column algorithm by Eisenstat, Gilbert and Liu, which includes Eisenstat and Liu's symmetric structural reduction for fast symbolic factorization. Our key contribution is to develop both numeric and symbolic schemes to perform supernode-panel updates to achieve better data reuse in cache and floating-point registers. A further refinement, a two-dimensional matrix partitioning scheme, enhances performance for large matrices or machines with small caches. We conduct extensive performance evaluations on several recent superscalar architectures, such as the IBM RS/6000-590, MIPS R8000 and DEC Alpha 21164, and show that our algorithm is much faster than its predecessors. The advantage is particularly evident for large problems. In addition, we develop a detailed model to systematically choose a set of blocking parameters in the algorithm. The second part focuses on the design, implementation and performance analysis of a shared memory parallel algorithm based on our new serial algorithm. We parallelize the computation along the column dimension of the matrix, assigning one block of columns (a panel) to a processor. The parallel algorithm retains the serial algorithm's ability to reuse cached data. We develop a dynamic scheduling mechanism to schedule tasks onto available processors. One merit of this approach is the ability to balance work load automatically. The algorithm attempts to schedule independent tasks to different processors. When this is not possible in the later stage of factorization, a pipeline approach is used to coordinate dependent computations. We demonstrate that the new parallel algorithm is very efficient on shared memory machines with modest numbers of processors, such as the SGI Power Challenge, DEC AlphaServer 8400, and Cray C90/J90. We also develop performance models to study available concurrency and identify performance bottlenecks."

Author: James W. Demmel
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 43

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Abstract: "Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines, because of its dynamic and somewhat unpredictable way of generating work and intermediate results at run time. In this paper, we present an efficient parallel algorithm that overcomes this difficulty. The high performance of our algorithm is achieved through (1) using a graph reduction technique and a supernode-panel computational kernel for high single processor utilization, and (2) scheduling two types of parallel tasks for a high level of concurrency. One such task is factoring the independent panels on the disjoint subtrees in the column elimination tree of A. Another task is updating a panel by previously computed supernodes. A scheduler assigns tasks to free processors dynamically and facilitates the smooth transition between the two types of parallel tasks. No global synchronization is used in the algorithm. The algorithm is well suited for shared memory machines (SMP) with a modest number of processors. We demonstrate 4-7 fold speedups on a range of 8 processor SMPs, and more on larger SMPs. One realistic problem arising from a 3-D flow calculation achieves factorization rates of 1.0, 2.5, 0.8 and 0.8 Gigaflops, on the 12 processor Power Challenge, 8 processor Cray J90, 16 processor Cray J90, and 8 processor AlphaServer 8400, respectively."

Author: M. Cosnard (Michel.)
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 584

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Progressing from theory to implementation, the text develops the algorithms of vector processors, shared-memory parallel machines and distributed-memory machines emphasising the link between architectures, models and algorithms. In addition, the book addresses a number of issues that are of great practical importance to people developing parallel programs, including coverage of LINPACK and BLAS, vectorisation, task placement and scheduling.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 7

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Book Description
We report our experiences with the Gauss elimination algorithm on several parallel machines. Several different software designs are demonstrated, ranging from a simple shared memory implementation to use of a message passing programming model. In this work we find that the efficient use of local memory is critical to obtaining good performance on scalable machines. Machines with large coherent caches appear to require the least software effort in order to obtain effective performance. 3 refs., 1 fig., 2 tabs.

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.

Author: Gregory A. Darmohray
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 216

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Book Description

Author: George Antoniou
Publisher: World Scientific
ISBN: 9810247591
Category : Computers
Languages : en
Pages : 497

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Book Description
This book is a balanced presentation of the latest techniques, algorithms and applications in computer science and engineering. The papers, written by eminent researchers in their fields, provide a vehicle for new research and development.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)