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arXiv 1801.04723cs.DC
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SPIN:Apache Spark中一种快速可扩展的矩阵求逆方法

SPIN: A Fast and Scalable Matrix Inversion Method in Apache Spark

Chandan Misra, Sourangshu Bhattacharya, Soumya K. Ghosh

摘要:

大数据在诸如地球科学、社交网络、物理科学等领域中的增长导致了对高效且可扩展的线性代数运算(例如,矩阵求逆)的巨大需求。使用大数据平台进行高效和分布式矩阵求逆的现有方法依赖于基于LU分解的块递归算法。然而,这些算法是复杂的,需要大量的边计算,例如矩阵乘法,在各种级别的递归。在本文中,我们提出了一个不同的计划的基础上Strassen的矩阵求逆算法(在Strassen的原始文件在1969年提到),它使用少得多的操作,在每一级的递归。我们实现了所提出的算法,并通过大量的实验,表明它是更有效的比最先进的方法。此外,我们提供了一个详细的理论分析所提出的算法,并推导出理论上的运行时间密切配合的经验观察挂钟运行时间,从而解释了U形行为w.r.t.块大小。

英文摘要:

The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and distributed matrix inversion using big data platforms rely on LU decomposition based block-recursive algorithms. However, these algorithms are complex and require a lot of side calculations, e.g. matrix multiplication, at various levels of recursion. In this paper, we propose a different scheme based on Strassen's matrix inversion algorithm (mentioned in Strassen's original paper in 1969), which uses far fewer operations at each level of recursion. We implement the proposed algorithm, and through extensive experimentation, show that it is more efficient than the state of the art methods. Furthermore, we provide a detailed theoretical analysis of the proposed algorithm, and derive theoretical running times which match closely with the empirically observed wall clock running times, thus explaining the U-shaped behaviour w.r.t. block-sizes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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