For the saddle-point problems, we discuss and analyze the updated preconditioned Hermitian and skew-Hermitian splitting (UPHSS) iteration method in detail. On this basis, we introduce a two-stage iteration method for the UPHSS iteration method. Theoretical analysis shows that the UPHSS and two-stage UPHSS iteration methods are convergent to the unique solution of the saddle-point linear system when the parameter is suitably chosen. Numerical examples show the correctness of the theory and the effectiveness of these methods.
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Supported by The National Natural Science Foundation (no. 11501038), and The Science and Technology Planning Projects of Beijing Municipal Education Commission (no. KM201911232010, no. KM202011232019 and no. KM201811232020), People’s Republic of China.
Communicated by Zhong-Zhi Bai.
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Chen, F., Li, T. & Lu, K. Updated preconditioned Hermitian and skew-Hermitian splitting-type iteration methods for solving saddle-point problems. Comp. Appl. Math. 39, 162 (2020). https://doi.org/10.1007/s40314-020-01187-7
- Saddle-point linear problem
- Hermitian and skew-Hermitian splitting
- Matrix splitting iteration
Mathematics Subject Classification