In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate and use these results to provide sharp estimates for the expected error reduction per iteration. We also study the fault-tolerant features of the randomized successive subspace correction method by rejecting corrections when faults occur and show that the resulting iterative method converges with probability one. In addition, we derive estimates on the expected convergence rate for the fault-tolerant, randomized, subspace correction method.

中文翻译：

---

子空间校正的随机容错方法

在本文中，我们考虑了具有随机顺序的子空间校正的迭代方法。我们证明了预期收敛速度的身份，并使用这些结果为每次迭代的预期误差减少提供了清晰的估计。我们还通过拒绝出现故障时的校正来研究随机连续子空间校正方法的容错特性，并证明了所得的迭代方法收敛于概率1。此外，我们得出了容错，随机子空间校正方法的预期收敛速度的估计值。