On semi-convergence of generalized skew-Hermitian triangular splitting iteration methods for singular saddle-point problems

摘要

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