Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems

An algorithm for solving a nonsingular symmetric system of linear equations with a saddle point is examined. This algorithm has two constant iteration parameters and is an extension of the algorithm of Hermitian and skew-Hermitian splitting iterations (the HSS algorithm). Analytical formulas are derived for the optimal values of the iteration parameters. The formulation of the optimization problem is a classical one for the saddle-point problems. The results obtained are sharp.