A preconditioner based on the shift-splitting method for generalized saddle point problems
This work addresses the need for efficient preconditioners for solving saddle point problems arising in scientific computing, but the contribution appears incremental as it extends existing shift-splitting techniques to a specific class of problems.
The authors propose a preconditioner for generalized saddle point problems based on the shift-splitting method, demonstrating unconditional convergence of the underlying iterative method and effectiveness through numerical experiments.
In this paper, we propose a preconditioner based on the shift-splitting method for generalized saddle point problems with nonsymmetric positive definite (1,1)-block and symmetric positive semidefinite $(2,2)$-block. The proposed preconditioner is obtained from an basic iterative method which is unconditionally convergent. We also present a relaxed version of the proposed method. Some numerical experiments are presented to show the effectiveness of the method.