A generalization of the HSS-based sequential two-stage method for solving non-Hermitian saddle point problems

作者：Chen, Cairong; Ma, Changfeng^*

来源：Numerical Algorithms, 2016, 73(4): 1073-1090.

DOI：10.1007/s11075-016-0130-y

• Non-Hermitian saddle-point problems
• Hermitian or skew-Hermitian dominant
• Hermitian and skew-Hermitian splitting (HSS)
• Two-stage method
• Preconditioner
• Convergence

For non-Hermitian saddle point problems with non-Hermitian positive definite (1,1)-block, Zhu et al. studied the HSS-based sequential two-stage method (see Zhu et al. Appl. Math. Comput. 242, 907-916 19). However, this approach may not work when the (1,1)-block of the saddle point problems is weakly Hermitian or skew-Hermitian dominant. By introducing a new preconditioning matrix, a generalization of the HSS-based sequential two-stage method is proposed for solving non-Hermitian saddle-point problems with non-Hermitian positive definite and Hermitian or skew-Hermitian dominant (1,1)-block. Theoretical analysis shows that the proposed iterative method is convergent. Numerical experiments are provided to confirm the theoretical results, which demonstrate that the generalized method is effective and feasible for solving saddle point problems with non-Hermitian positive definite and Hermitian or skew-Hermitian dominant (1,1)-block.

• 出版日期2016-12
• 单位福建师范大学