| Citation: |
Jiyu Wang, Xiuling Jia, Cuixia Li, Shiliang Wu. A NEW APPROACH FOR LINEAR SYSTEMS OF THE FORM (A + γUUT)X = B[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1719-1735. doi: 10.11948/20250099
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A NEW APPROACH FOR LINEAR SYSTEMS OF THE FORM (A + γUUT)X = B
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Abstract
In this paper, we consider the numerical solution of linear systems of the form (A + γUUT)x = b. A new approach for this linear systems is proposed: by transforming this linear systems into the equivalent saddle point problem, we propose a new and effective preconditioner for this equivalent saddle point form and discuss the spectral properties of the corresponding preconditioned matrix. When dealing with the associated residual equations, compared with some existing preconditioners, the proposed precondnitioner can save computational workload, running time and computer memory in actual implementations. To illustrate the performance of the proposed preconditioner, some examples from different application cases are provided. Moreover, compared with some existing preconditioning strategies, the numerical results show that the proposed preconditioner is more competitive in a way.
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Keywords:
- Linear systems /
- saddle point problem /
- preconditioner /
- Krylov subspace method
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References
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Jiyu Wang, Xiuling Jia, Cuixia Li, Shiliang Wu. A NEW APPROACH FOR LINEAR SYSTEMS OF THE FORM (A + γUUT)X = B[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1719-1735. doi: 10.11948/20250099
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Figure 1.
Spectra of
$ P^{-1}_{\alpha}A_{\gamma} $ $ P_{\beta}^{-1}\mathcal{A} $ $ \gamma=0.001 $ $ \gamma=0.005 $ $ \gamma=0.01 $ -
Figure 2.
Spectra of
$ P^{-1}_{\alpha}A_{\gamma} $ $ P_{\beta}^{-1}\mathcal{A} $ $ \gamma=0.1 $ $ \gamma=1 $ $ \gamma=10 $ -
Figure 3.
Spectra of
$ P^{-1}_{\alpha}A_{\gamma} $ $ P_{\beta}^{-1}\mathcal{A} $ $ \gamma=0.1 $ $ \gamma=1 $ $ \gamma=10 $