Semi-convergence of the EPSS method for singular generalized saddle point problems

Abstract: Recently, in (M. Masoudi, D.K. Salkuyeh, An extension of positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems, Computers & Mathematics with Application, https://doi.org/10.1016/j.camwa.2019.10.030, 2019) an extension of the positive definite and skew-Hermitian splitting (EPSS) iteration method for nonsingular generalized saddle point problems has been presented. In this article, we study semi-convergence of the EPSS method for singular generalized saddle problems. Then a special case of EPSS (SEPSS) preconditioner is applied to the nonsingular generalized saddle point problems. Some numerical results are presented to show the effectiveness of the preconditioner.