  In this paper we apply the stochastic variance reduced gradient (SVRG)
method, which is a popular variance reduction method in optimization for
accelerating the stochastic gradient method, to solve large scale linear
ill-posed systems in Hilbert spaces. Under {\it a priori} choices of stopping
indices, we derive a convergence rate result when the sought solution satisfies
a benchmark source condition and establish a convergence result without using
any source condition. To terminate the method in an {\it a posteriori} manner,
we consider the discrepancy principle and show that it terminates the method in
finite many iteration steps almost surely. Various numerical results are
reported to test the performance of the method.
