Generalized Skew-Hermitian Triangular Splitting Iteration Methods For Singular Saddle-point Problems

Large sparse linear systems of saddle-point structure are of important practi-cal significance, for they arise in many scientific and-engineering applications. For solving these problems, many effective iteration methods and preconditioning tech-niques have been proposed. However, most of these methods are mainly used to solve the nonsingular saddle-point problems. So it needs further research to general-ize the effective iteration methods for nonsingular saddle-point problems to singular saddle-point problems and analyze their semi-convergence properties.In 2014, Krukier et al. proposed an efficient generalized skew-Hermitian trian-gular 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 GST-S method are analyzed by using singular value decomposition and Moore-Penrose inverse, under suitable restrictions on the involved iteration parameters.Finally, numerical results are presented to demonstrate the feasibility and effi-ciency of the GSTS iteration methods, both used as solvers and preconditioners for GMRES method.