随机拟面算法的误差界分析

K. Pentland, M. Tamborrino, Timothy John Sullivan
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引用次数: 0

摘要

随机并行并行算法(parareal)是流行的并行实时算法(parareal)的一种概率变体。与平行相似,它使用预测校正器(PC)方案组合了常微分方程(ODE)的细粒度和粗粒度解。关键的区别在于,仔细选择的随机扰动被添加到PC中,以试图加速ODE随机解的位置。在本文中,我们导出了应用于不同类型扰动的非线性微分方程系统的超线性和线性均方误差界。我们在线性ODE系统和标量非线性ODE系统上对这些边界进行了数值说明,证明了理论与数值之间的良好匹配。
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Error bound analysis of the stochastic parareal algorithm
Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a predictor-corrector (PC) scheme. The key difference is that carefully chosen random perturbations are added to the PC to try to accelerate the location of a stochastic solution to the ODE. In this paper, we derive superlinear and linear mean-square error bounds for SParareal applied to nonlinear systems of ODEs using different types of perturbations. We illustrate these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE, showing a good match between theory and numerics.
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