Randomized and fault-tolerant method of subspace corrections
Randomized and fault-tolerant method of subspace corrections
复制标题
DOI：
10.1007/s40687-019-0187-z
复制
发表时间：
2019-08
影响因子：
1.2
通讯作者：
Xiaozhe Hu;Jinchao Xu;L. Zikatanov
中科院分区：
文献类型：
--
作者：
Xiaozhe Hu;Jinchao Xu;L. Zikatanov
本文考虑带随机序的子空间修正的迭代方法。我们证明了期望收敛速度的恒等式，并利用这些结果为每次迭代的期望误差减少提供了精确的估计。我们还研究了随机化连续子空间校正方法的容错特性，当故障发生时拒绝校正，并证明了所得到的迭代方法以概率1收敛。此外，我们还得到了容错随机子空间校正方法的期望收敛速度的估计。
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.