论文标题
使用低精度近似随机变量舍入误差
Rounding error using low precision approximate random variables
论文作者
论文摘要
对于使用Euler-Maruyama方案到随机微分方程的数值近似值，我们提出了使用低精度（例如单个和一半精度）计算出的近似随机变量。我们提出并证明了发生的舍入误差的模型，并产生针对两条和四种方式差异的平均情况误差，适用于常规和嵌套的多层次蒙特卡洛估计。通过在有或没有Kahan补偿的各种精确度中考虑多级蒙特卡洛校正项的方差结构，我们计算了各种精确度中提供的潜在速度UPS。我们发现，在广泛的离散水平上，单个精度为近似速度提高了7倍的可能性。一半的精度为几个粗大的模拟提供了可比的改进，甚至在最粗糙的几个级别上，甚至可以提供10-12倍的改进。
For numerical approximations to stochastic differential equations using the Euler-Maruyama scheme, we propose incorporating approximate random variables computed using low precisions, such as single and half precision. We propose and justify a model for the rounding error incurred, and produce an average case error bound for two and four way differences, appropriate for regular and nested multilevel Monte Carlo estimations. By considering the variance structure of multilevel Monte Carlo correction terms in various precisions with and without a Kahan compensated summation, we compute the potential speed ups offered from the various precisions. We find single precision offers the potential for approximate speed improvements by a factor of 7 across a wide span of discretisation levels. Half precision offers comparable improvements for several levels of coarse simulations, and even offers improvements by a factor of 10-12 for the very coarsest few levels.
