Parallel Solution of Dense Linear Systems on the k-Ary n-Cube Networks

A. Al-Ayyoub, K. Day
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引用次数: 5

Abstract

In this paper a parallel algorithm for solving systems of linear equation on the k-ary n-cube is presented and evaluated for the first time. The proposed algorithm is of O(N3/kn) computation complexity and uses O(Nn) communication time to factorize a matrix of order N on the k-ary n-cube. This is better than the best known results for the hypercube, O(N log kn), and the mesh, , each with approximately kn nodes. The proposed parallel algorithm takes advantage of the extra connectivity in the k-ary n-cube in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.
k-Ary n-Cube网络上密集线性系统的并行解
本文首次给出了求解k元n立方上线性方程组的一种并行算法,并对其进行了评价。该算法的计算复杂度为O(N3/kn),使用O(Nn)通信时间在k元N立方上分解N阶矩阵。这比最著名的超立方体(O(N log kn))和网格(每个都有大约kn个节点)的结果要好。所提出的并行算法利用了k元n立方中额外的连通性,以减少诸如旋转、行/列交换以及主行和乘法器列广播等任务所涉及的通信时间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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