Stochastic subspace correction in Hilbert space
For researchers in numerical analysis and machine learning, this work provides a theoretical improvement over existing incremental approximation methods.
The paper proposes a stochastic subspace correction method for solving variational problems in infinite-dimensional Hilbert spaces, achieving convergence rates for the expected squared error under weaker conditions than previously known.
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is solved. we show that convergence rates for the expectation of the squared error can be guaranteed under weaker conditions than previously established in [Constr. Approx. 44:1 (2016), 121-139]. A connection to the theory of learning algorithms in reproducing kernel Hilbert spaces is revealed.