并行矩阵向量积的近似层次方法

A. Grama, Vipin Kumar, A. Sameh
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引用次数: 10

摘要

矩阵-向量积(mat-vecs)是求解密集线性系统的迭代方法的核心。通常,这些系统出现在电磁学、热传导和波传播中使用的积分方程的解中。本文给出了一种求解积分方程中栅格向量的并行近似方法。我们使用这种方法来计算包含数十万个元素的密集网格。使用近似方法和并行处理获得的联合加速比单处理器上的精确mat-vec提高了几个数量级。我们证明,我们的并行公式产生最小的并行处理开销,并扩展到大量处理器。我们研究了改变近似矩阵的精度对总时间和并行效率的影响。给出了256处理器Cray T3D和Thinking Machines CM5并行计算机的实验结果。我们已经在T3D上实现了超过5 GFLOPS的计算速率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Parallel Matrix-Vector Product Using Approximate Hierarchical Methods
Matrix-vector products (mat-vecs) form the core of iterative methods used for solving dense linear systems. Often, these systems arise in the solution of integral equations used in electromagnetics, heat transfer, and wave propagation. In this paper, we present a parallel approximate method for computing mat-vecs used in the solution of integral equations. We use this method to compute dense mat-vecs of hundreds of thousands of elements. The combined speedups obtained from the use of approximate methods and parallel processing represent an improvement of several orders of magnitude over exact mat-vecs on uniprocessors. We demonstrate that our parallel formulation incurs minimal parallel processing overhead and scales up to a large number of processors. We study the impact of varying the accuracy of the approximate mat-vec on overall time and on parallel efficiency. Experimental results are presented for 256 processor Cray T3D and Thinking Machines CM5 parallel computers. We have achieved computation rates in excess of 5 GFLOPS on the T3D.
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