Efficient parameterized rotated shift-splitting preconditioner for a class of complex symmetric linear systems
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By utilizing the equivalent real block two-by-two linear systems and the shift-splitting techniques, we establish an efficient parameterized rotated shift-splitting (PRSS) preconditioner for solving a class of complex symmetric linear systems. The proposed preconditioner is extracted from a stationary iteration method which is unconditionally convergent. Moreover, some spectral properties of the corresponding preconditioned matrix are studied in detail. Finally, numerical results are presented to show the feasibility and effectiveness of the proposed preconditioner.
KeywordsComplex symmetric linear systems Parameterized rotated shift-splitting preconditioner Spectral properties
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The authors would like to thank the editor and the anonymous referees for their detailed comments which greatly improve the presentation. This research is supported by National Science Foundation of China (41725017, 41590864), National Basic Research Program of China under grant number 2014CB845906. It is also partially supported by the CAS/CAFEA international partnership Program for creative research teams (No. KZZD-EW-TZ-19 and KZZD-EW-TZ-15), Strategic Priority Research Program of the Chinese Academy of Sciences (XDB18010202) and Fujian Natural Science Foundation (2016J01005).