A fast iteration method based on HSS is proposed for solving the nonsymmetric generalized saddle point problem. It converges to the unique solution of the generalized saddle point problem unconditionally. We devise a new preconditioner induced by the new iteration method. We analyze the spectrum of the preconditioned coefficient matrix, and reveal the relation between the theoretically required number of iteration steps and the dimension of the preconditioned Krylov subspace. Furthermore, some practical inexact variants of the new preconditioner have been developed to reduce the computational overhead. Numerical experiments validate the effectiveness of the proposed preconditioners.

提出了一种基于HSS的快速迭代方法来解决非对称广义鞍点问题。它无条件地收敛到广义鞍点问题的唯一解。我们设计了一种由新的迭代方法引入的新的预处理器。我们分析了预处理系数矩阵的频谱，并揭示了理论上需要的迭代步数与预处理Krylov子空间维数之间的关系。此外，已经开发了新的预处理器的一些实际的不精确变体以减少计算开销。数值实验验证了所提出的预处理器的有效性。