In this work, we collect data from runs of Krylov subspace methods and pipelined Krylov algorithms in an effort to understand and model the impact of machine noise and other sources of variability on performance. We find large variability of Krylov iterations between compute nodes for standard methods that is reduced in pipelined algorithms, directly supporting conjecture, as well as large variation between statistical distributions of runtimes across iterations. Based on these results, we improve upon a previously introduced nondeterministic performance model by allowing iterations to fluctuate over time. We present our data from runs of various Krylov algorithms across multiple platforms as well as our updated non-stationary model that provides good agreement with observations. We also suggest how it can be used as a predictive tool.

中文翻译：

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了解标准和流水线并行Krylov求解器中的性能可变性

在这项工作中，我们从Krylov子空间方法和流水线Krylov算法的运行中收集数据，以了解和建模机器噪声和其他可变性对性能的影响。对于流水线算法中减少的标准方法，我们发现计算方法之间的Krylov迭代之间存在很大的差异，这直接支持了推测，而且跨迭代的运行时统计分布之间也存在较大的差异。基于这些结果，我们通过允许迭代随时间波动来改进先前引入的不确定性性能模型。我们提供了跨多个平台运行的各种Krylov算法的数据，以及更新后的非平稳模型，该模型与观测值具有很好的一致性。我们还建议如何将其用作预测工具。