  Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting
iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl.
21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular
splitting (GSTS) iteration method for nonsingular saddle-point linear systems
with strong skew-Hermitian parts. In this work, we further use the GSTS method
to solve singular saddle-point problems. The semi-convergence properties of
GSTS method are analyzed by using singular value decomposition and
Moore-Penrose inverse, under suitable restrictions on the involved iteration
parameters. Numerical results are presented to demonstrate the feasibility and
efficiency of the GSTS iteration methods, both used as solvers and
preconditioners for GMRES method.
