Abstract
For solving a class of complex symmetric system of linear equations, we apply the minimum residual technique to the modified Hermitian and skew-Hermitian splitting (MHSS) iteration scheme and propose an iteration method referred to as minimum residual MHSS (MRMHSS) iteration method. Compared with the classical MHSS method, the MRMHSS method has two more iteration parameters, which can be automatically and easily computed. Then, some properties of the MRMHSS iteration method are carefully studied. Finally, we use four examples to test the performance of the MRMHSS iteration method by comparing its numerical results with three other iteration methods.
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Acknowledgments
The authors would like to thank the referees for comments that lead to improvements of the presentation.
Funding
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11401281, 11471150) and the China Scholarship Council (CSC No. 201806180081).
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Zhang, WH., Yang, AL. & Wu, YJ. Minimum residual modified HSS iteration method for a class of complex symmetric linear systems. Numer Algor 86, 1543–1559 (2021). https://doi.org/10.1007/s11075-020-00944-3
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DOI: https://doi.org/10.1007/s11075-020-00944-3
Keywords
- Complex symmetric matrix
- Modified Hermitian and skew-Hermitian splitting iteration method
- Minimum residual technique
- Convergence property
- Iteration parameter