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For nonsymmetric saddle point problems, Huang et al. in (Numer. Algor. 2016, doi: 10.1007/s11075-016-0236-2) established a generalized variant of the deteriorated positive semi-definite and skew-Hermitian splitting (GVDPSS) preconditioner to expedite the convergence speed of the Krylov subspace iteration methods like the GMRES method. In this paper, some new convergence properties as well as some new numerical results are presented to validate the theoretical results. Mathematics subject classification: 65F10, 65N22.

On the Generalized Deteriorated Positive Semi-Definite and Skew-Hermitian Splitting Preconditioner