Converagence of randomized Douglas-Rachford method for linear system

In this article, we propose a randomized Douglas-Rachford(DR) method for linear system. This algorithm is based on the cyclic DR method. We consider a linear system as a feasible problem of finding intersection of hyperplanes. In each iteration, the next iteration point is determined by a random DR operator. We prove the convergence of the iteration points based on expectation. And the variance of the iteration points declines to zero. The numerical experiment shows that the proposed algorithm performs better than the cyclic DR method.