Randomized Method of Subspace Corrections
Provides theoretical guarantees for randomized iterative methods in numerical linear algebra, relevant for large-scale and fault-prone computing.
The paper proves identities for the expected convergence rate of randomized subspace correction methods and shows that a fault-tolerant variant converges with probability one, providing sharp error reduction estimates.
In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the fault-tolerant feature of the randomized successive subspace correction method by simply rejecting all the corrections when error occurs and show that the results iterative method converges with probability one. Moreover, we also provide sharp estimates on the expected convergence rate for the fault-tolerant, randomized, subspace correction method.