In this paper, we execute the shift-splitting preconditioner for asymmetric saddle point problems with its (1,2) block’s transposition unequal to its (2,1) block under the removed minus of its (2,1) block. The proposed preconditioner is stemmed from the shift splitting (SS) iteration method for solving asymmetric saddle point problems, which is convergent under suitable conditions. The relaxed version of the shift-splitting preconditioner is obtained as well. The spectral distributions of the related preconditioned matrices are given. Numerical experiments from the Stokes problem are offered to show the convergence performance of these two preconditioners.

在本文中，我们针对不对称鞍点问题执行移位拆分预处理器，其（1,2）块的移位不等于（2,1）块的负负，而其（2,1）块的移位不等于（2,1）块。提出的预处理器源于用于解决非对称鞍点问题的移位分裂（SS）迭代方法，该方法在合适的条件下收敛。还获得了移位分离预处理器的放松版本。给出了相关预处理矩阵的光谱分布。通过Stokes问题进行的数值实验表明了这两个预处理器的收敛性能。