Author: Y. Saad
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
This paper proposes a few lower bounds for communication complexity of the Gaussian Elimination algorithm on multiprocessors. Three types of architectures are considered: a bus architecture, a nearest neighbor ring network and a nearest neighbor grid network. Additional keywords: Computations, and Grids.
Author: Youcef Saad
Publisher:
ISBN:
Category : Parallel processing (Electronic computers)
Languages : en
Pages : 34
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Book Description
Proposes lower bounds for communication complexity of the Gaussian Elimination algorithm on multiprocessors.
Author: Gregory A. Darmohray
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 216
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Book Description
Author: S. Venkatesan
Publisher:
ISBN:
Category :
Languages : en
Pages : 144
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Book Description
Author: Abdel Krim Amoura
Publisher:
ISBN:
Category : Directed graphs
Languages : en
Pages : 18
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Book Description
Author: Vijay K. Naik
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 232
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Book Description
Multiprocessing: Trade-Offs in Computation and Communication presents an in-depth analysis of several commonly observed regular and irregular computations for multiprocessor systems. This book includes techniques which enable researchers and application developers to quantitatively determine the effects of algorithm data dependencies on execution time, on communication requirements, on processor utilization and on the speedups possible. Starting with simple, two-dimensional, diamond-shaped directed acyclic graphs, the analysis is extended to more complex and higher dimensional directed acyclic graphs. The analysis allows for the quantification of the computation and communication costs and their interdependencies. The practical significance of these results on the performance of various data distribution schemes is clearly explained. Using these results, the performance of the parallel computations are formulated in an architecture independent fashion. These formulations allow for the parameterization of the architecture specitific entities such as the computation and communication rates. This type of parameterized performance analysis can be used at compile time or at run-time so as to achieve the most optimal distribution of the computations. The material in Multiprocessing: Trade-Offs in Computation and Communication connects theory with practice, so that the inherent performance limitations in many computations can be understood, and practical methods can be devised that would assist in the development of software for scalable high performance systems.
Author: International Computer Science Institute
Publisher:
ISBN:
Category : Gaussian processes
Languages : en
Pages : 24
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Book Description
Abstract: "Consider the Gaussian Elimination algorithm with the well-known Partial Pivoting strategy for improving numerical stability (GEPP). Vavasis proved that the problem of determining the pivot sequence used by GEPP is log space-complete for P, and thus inherently sequential. Assuming P [not =] NC, we prove here that either the latter problem cannot be solved in parallel time O(N[superscript 1/2 - [epsilon]]) or all the problems in P admit polynomial speedup. Here N is the order of the input matrix and [epsilon] is any positive constant. This strengthens the P- completeness result mentioned above. We conjecture that the result proved in this paper holds for the stronger bound O(N[superscript 1- [epsilon]]) as well, and provide supporting evidence to the conjecture. Note that this is equivalent to assert the asymptotic optimality of the naive parallel algorithm for GEPP (modulo P [not =] NC)."
Author: I. C. F. Ipsen
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
Different algorithms, based on Gaussian elimination, for the solution of dense linar systems of equations, are discussed for a multiprocessor ring. The number of processors is assumed not to exceed the problem size. A fairly general model for data transfer is proposed and the algorithms are analysed with respect to their requirements of arithmetic as well as communication times. This paper lays no claims to being either exhaustive or complete. Its objective is to compare a variety of algorithms, which are fairly reasonable to program and to analyse, for the solution of a single problem on a certain class of parallel architectures, thereby leading to a more realistic approach to future algorithm development on multiprocessor machines.
Author: Yousef Saad
Publisher:
ISBN:
Category : Multiprocessors
Languages : en
Pages : 23
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Book Description
This paper proposes several implementations of Gaussian elimination for solving banded linear systems on multiprocessors. Three simple architectures are considered: a multiprocessor ring, a grid array and a hypercube. The complexity analysis fully accounts for communication delays by using simple models where both latency and actual transfer times are incorporated. When the number of processors is small relative to the bandwidth of the system a row interleaved implementation of Gaussian elimination algorithm is attractive. Otherwise, a two-dimensional grid is essential for achieving higher speed-up. The hypercube architecture gives the smallest communication latency times. (Author).
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.
