| Citation: |
Wenbin Bao, Shuxin Miao. A MODIFIED BLOCK PRECONDITIONER FOR COMPLEX SYMMETRIC INDEFINITE LINEAR SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 182-196. doi: 10.11948/20230131
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A MODIFIED BLOCK PRECONDITIONER FOR COMPLEX SYMMETRIC INDEFINITE LINEAR SYSTEMS
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Abstract
To solve the real equivalent $ 2\times 2 $ block linear system of complex symmetric indefinite linear systems, by introducing a preconditioning matrix in the NB preconditioner (which was proposed in [Numerical Algorithm, 74 (2017) 889-903]), a modified block preconditioner is proposed. Compared with the NB one, when choose a suitable preconditioning matrix for the new preconditioner to get faster convergence than the NB preconditioner. The unconditional convergence of the new iteration method is discussed. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are given. Finally, a numerical example is carried out to demonstrate the effectiveness and robustness of the proposed preconditioner.
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References
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Wenbin Bao, Shuxin Miao. A MODIFIED BLOCK PRECONDITIONER FOR COMPLEX SYMMETRIC INDEFINITE LINEAR SYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 182-196. doi: 10.11948/20230131
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Figure 1.
Residual curves of different preconditioned iteration methods for Example 4.1:
$ 32\times 32 $ $ 48\times 48 $ -
Figure 2.
The eigenvalue distributions of preconditioned matrices for Example 4.1