  This paper provides a comprehensive discussion of the equivalences between
splitting methods. These equivalences have been studied over the past few
decades and, in fact, have proven to be very useful. In this paper, we survey
known results and also present new ones. In particular, we provide simplified
proofs of the equivalence of the ADMM and the Douglas-Rachford method and the
equivalence of the ADMM with intermediate update of multipliers and the
Peaceman-Rachford method. Other splitting methods are also considered.
