Numerically Stable Polynomially Coded Computing
Numerically Stable Polynomially Coded Computing
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DOI：
10.1109/isit.2019.8849468
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发表时间：
2019-03
期刊：
影响因子：
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通讯作者：
Mohammad Fahim;V. Cadambe
中科院分区：
文献类型：
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作者：
Mohammad Fahim;V. Cadambe
我们认为在分布式系统中的工作节点容易出现故障/延迟的编码大规模矩阵乘法问题的数值稳定性的问题。我们构建新的代码，实现可比容错以前的代码，但更数字稳定。与以前的代码，使用多项式扩展在单项式的基础上，我们的代码使用多项式表示的正交多项式的基础上。我们表明，通过新的理论结果的条件数，以及数值实验，这些代码的应用可以导致显着更数值稳定的计算比目前的单项基代码。
We consider the issue of numerical stability in solving the problem of coded large scale matrix multiplication in distributed systems where worker nodes are prone to failures/delays. We construct new codes that achieve comparable fault tolerance as previous codes, but are more numerically stable. Unlike previous codes that use polynomials expanded in a monomial basis, our codes use polynomials expressed in a basis of orthonormal polynomials. We show via new theoretical results on the condition number, as well as numerical experiments, that the application of these codes can lead to significantly more numerically stable computation than the current monomial-basis codes.