An improved block splitting preconditioner for complex symmetric indefinite linear systems |
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| Authors: | Ju-Li Zhang Hong-Tao Fan Chuan-Qing Gu |
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| Affiliation: | 1.School of Fundamental Studies,Shanghai University of Engineering Science,Shanghai,People’s Republic of China;2.Department of Mathematics,Zhejiang A&F University,Zhejiang,People’s Republic of China;3.School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems,Lanzhou University,Lanzhou,People’s Republic of China;4.Department of Mathematics,Shanghai University,Shanghai,People’s Republic of China |
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| Abstract: | In this paper, an improved block splitting preconditioner for a class of complex symmetric indefinite linear systems is proposed. By adopting two iteration parameters and the relaxation technique, the new preconditioner not only remains the same computational cost with the block preconditioners but also is much closer to the original coefficient matrix. The theoretical analysis shows that the corresponding iteration method is convergent under suitable conditions and the preconditioned matrix can have well-clustered eigenvalues around (0,1) with a reasonable choice of the relaxation parameters. An estimate concerning the dimension of the Krylov subspace for the preconditioned matrix is also obtained. Finally, some numerical experiments are presented to illustrate the effectiveness of the presented preconditioner. |
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