On preconditioned MHSS iteration methods for complex symmetric linear systems |
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| Authors: | Zhong-Zhi Bai Michele Benzi Fang Chen |
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| Institution: | 1.State Key Laboratory of Scientific/Engineering Computing,Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing,People’s Republic of China;2.Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing,People’s Republic of China;3.Department of Mathematics and Computer Science,Emory University,Atlanta,USA;4.School of Science,Xi’an University of Post and Telecommunications,Xi’an,People’s Republic of China |
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| Abstract: | We propose a preconditioned variant of the modified HSS (MHSS) iteration method for solving a class of complex symmetric systems of linear equations. Under suitable conditions, we prove
the convergence of the preconditioned MHSS (PMHSS) iteration method and discuss the spectral properties of the PMHSS-preconditioned matrix. Numerical implementations show
that the resulting PMHSS preconditioner leads to fast convergence when it is used to precondition Krylov subspace iteration
methods such as GMRES and its restarted variants. In particular, both the stationary PMHSS iteration and PMHSS-preconditioned
GMRES show meshsize-independent and parameter-insensitive convergence behavior for the tested numerical examples. |
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