On equivalence of optimal relaxed block iterative methods for the singular nonsymmetric saddle point problem

There exist many classes of relaxed block iterative methods for the solution of the nonsingular and singular saddle point problems. Recently, the singular nonsymmetric saddle point problem has been optimally solved by means of a stationary linear second-order iterative method using the Manteuffel algorithm [Hadjidimos (2016) [19]]. The main purpose of this work is to extend, analyze and study a number of classes of stationary iterative methods based on generalizations of SOR-like methods, determine their optimal parameters, via the optimal parameters in the aforementioned work, and show the equivalence of the optimal methods studied. Finally, a computational comparison of the performances of the above optimal methods and their nonstationary counterparts shows the superiority of the latter methods.