A Distributed Eigensolver for Loosely Coupled Networks

H. Straková, W. Gansterer
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引用次数: 16

Abstract

We introduce a new distributed eigensolver (dOI) for square matrices based on orthogonal iteration. In contrast to standard parallel eigensolvers, our approach performs only nearest neighbor communication and provides much more flexibility with respect to the properties of the hardware infrastructure on which the computation is performed. This is achieved by utilizing distributed summation methods with randomized communication schedules which do not require global synchronization across the nodes. Our algorithm is particularly attractive for loosely coupled distributed networks with arbitrary network topologies and potentially unreliable components. Our distributed eigensolver dOI is based on a novel distributed matrix-matrix multiplication algorithm and on an extension of a distributed QR factorization algorithm proposed earlier. We illustrate the advantages of dOI in terms of higher flexibility with respect to the underlying network and lower communication cost compared to a related distributed eigensolver by Kempe and McSherry. Moreover, we experimentally illustrate how the overall communication cost of dOI is further reduced by adapting the accuracy of each distributed summation during the orthogonal iteration process.
松耦合网络的分布式特征解算器
提出了一种新的基于正交迭代的方阵分布特征求解器。与标准的并行特征求解器相比,我们的方法只执行最近邻通信,并且在执行计算的硬件基础设施的属性方面提供了更大的灵活性。这是通过使用具有随机通信调度的分布式求和方法实现的,该方法不需要跨节点的全局同步。我们的算法对于具有任意网络拓扑和潜在不可靠组件的松散耦合分布式网络特别有吸引力。我们的分布式特征求解器dOI基于一种新的分布式矩阵-矩阵乘法算法和先前提出的分布式QR分解算法的扩展。与Kempe和McSherry的相关分布式特征求解器相比,我们说明了dOI在相对于底层网络的更高灵活性和更低通信成本方面的优势。此外,我们通过实验说明了如何在正交迭代过程中通过调整每个分布求和的精度来进一步降低dOI的总体通信成本。
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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