  We use a unified framework to summarize sixteen randomized iterative methods
including Kaczmarz method, coordinate descent method, etc. Some new iterative
schemes are given as well. Some relationships with \textsc{mg} and \textsc{ddm}
are also discussed. We analyze the convergence properties of the iterative
schemes by using the matrix integrals associated with alternating projectors,
and demonstrate the convergence behaviors of the randomized iterative methods
by numerical examples.
