| Citation: |
Li-Tao Zhang, Ming-Qian Guo, Bing-Ran Tian, Guang-Xu Zhu, Xiao-Lu Wang, Hao-Chen Zhao. PARAMETERIZED REGULARIZED DPSS PRECONDITIONERS FOR NON-HERMITIAN SADDLE POINT PROBLEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 731-743. doi: 10.11948/20250175
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PARAMETERIZED REGULARIZED DPSS PRECONDITIONERS FOR NON-HERMITIAN SADDLE POINT PROBLEMS
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Abstract
Recently, Cao [Applied Mathematics Letters, 2018, 84: 96-102] presented a regularized deteriorated positive and skew-Hermitian splitting (RDPSS) iteration method for solving the large sparse non-Hermitian saddle point problems and studied the convergence of the corresponding RDPSS stationary iteration method. In this paper, based on the RDPSS iteration method, we construct a parameterized RDPSS (PRDPSS) iteration method for solving the large sparse non-Hermitian saddle point problems and theoretically prove that presented method converges to the unique solution of the system of linear equations unconditionally. Finally, one example is provided to confirm the effectiveness.
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Keywords:
- Non-Hermitian matrix /
- regularization /
- convergence /
- preconditioner /
- eigenvalue
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References
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Li-Tao Zhang, Ming-Qian Guo, Bing-Ran Tian, Guang-Xu Zhu, Xiao-Lu Wang, Hao-Chen Zhao. PARAMETERIZED REGULARIZED DPSS PRECONDITIONERS FOR NON-HERMITIAN SADDLE POINT PROBLEMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 731-743. doi: 10.11948/20250175
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Figure 1.
A uniform mesh with
$ h=\frac{\sqrt{2}}{4} $ -
Figure 2.
The eigenvalue distribution for the PRDPSS iteration matrix
$ \mathcal {M}_{\text{PRDPSS}}^{-1}\mathcal {N}_{\text{PRDPSS}} $ $ \alpha=0.1, \beta=0.2 $ $ \alpha=0.3, \beta=0.5 $ $ \alpha=0.5, \beta=0.3 $ $ \alpha=0.5, \beta=0.7 $ $ h=\frac{\sqrt{2}}{8} $ -
Figure 3.
The eigenvalue distribution for the RDPSS iteration matrix
$ \mathcal {M}_{\text{RDPSS}}^{-1}\mathcal {N}_{\text{RDPSS}} $ $ \alpha=0.1 $ $ \alpha=0.3 $ $ \alpha=0.5 $ $ \alpha=0.9 $ $ h=\frac{\sqrt{2}}{8} $ -
Figure 4.
The eigenvalue distribution for the PRDPSS iteration matrix
$ \mathcal {M}_{\text{PRDPSS}}^{-1}\mathcal {N}_{\text{PRDPSS}} $ $ \alpha=0.1, \beta=0.2 $ $ \alpha=0.3, \beta=0.5 $ $ \alpha=0.5, \beta=0.3 $ $ \alpha=0.5, \beta=0.7 $ $ h=\frac{\sqrt{2}}{12} $ -
Figure 5.
The eigenvalue distribution for the RDPSS iteration matrix
$ \mathcal {M}_{\text{RDPSS}}^{-1}\mathcal {N}_{\text{RDPSS}} $ $ \alpha=0.1 $ $ \alpha=0.3 $ $ \alpha=0.5 $ $ \alpha=0.9 $ $ h=\frac{\sqrt{2}}{12} $ -
Figure 6.
The eigenvalue distribution for the PRDPSS iteration matrix
$ \mathcal {M}_{\text{PRDPSS}}^{-1}\mathcal {N}_{\text{PRDPSS}} $ $ \alpha=0.1, \beta=0.2 $ $ \alpha=0.3, \beta=0.5 $ $ \alpha=0.5, \beta=0.3 $ $ \alpha=0.5, \beta=0.7 $ $ h=\frac{\sqrt{2}}{18} $ -
Figure 7.
The eigenvalue distribution for the RDPSS iteration matrix
$ \mathcal {M}_{\text{RDPSS}}^{-1}\mathcal {N}_{\text{RDPSS}} $ $ \alpha=0.1 $ $ \alpha=0.3 $ $ \alpha=0.5 $ $ \alpha=0.9 $ $ h=\frac{\sqrt{2}}{18} $