An inexact relaxed DPSS preconditioner for saddle point problem

Based on the relaxed deteriorated positive-definite and skew-Hermitian splitting (DPSS) preconditioner, in this paper, we proposed a class of relaxed deteriorated positive-definite and skew-Hermitian splitting (RDPSS) preconditioner for solving the saddle point problem. The proposed RDPSS preconditioner is a technical modification of the deteriorated positive-definite and skew-Hermitian splitting (DPSS) preconditioner [36]. The PSS preconditioner is a straightforward application of the positive-definite and skew-Hermitian splitting (PSS) iteration method for solving non-Hermitian positive definite linear systems initially established by Bai et al. [37]. Numerical results have shown that the proposed RDPSS preconditioner is advantageous over the existing DPSS preconditioner.