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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Supported by The National Natural Science Foundation for Innovative Research Groups (No. 11021101), The Hundred Talent Project of Chinese Academy of Sciences, The National Basic Research Program (No. 2011CB309703), P.R. China, and by the US National Science Foundation grant DMS-0810862.
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Bai, ZZ., Benzi, M. & Chen, F. On preconditioned MHSS iteration methods for complex symmetric linear systems. Numer Algor 56, 297–317 (2011). https://doi.org/10.1007/s11075-010-9441-6
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DOI: https://doi.org/10.1007/s11075-010-9441-6