TY - JOUR
T1 - Randomized and fault-tolerant method of subspace corrections
AU - Hu, Xiaozhe
AU - Xu, Jinchao
AU - Zikatanov, Ludmil T.
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2019/9/1
Y1 - 2019/9/1
N2 - 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.
AB - 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.
UR - http://link.springer.com/10.1007/s40687-019-0187-z
UR - http://www.scopus.com/inward/record.url?scp=85070679873&partnerID=8YFLogxK
U2 - 10.1007/s40687-019-0187-z
DO - 10.1007/s40687-019-0187-z
M3 - Article
SN - 2522-0144
VL - 6
JO - Research in Mathematical Sciences
JF - Research in Mathematical Sciences
IS - 3
ER -