On semi-convergence of parameterized SHSS method for a class of singular complex symmetric linear systems

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Abstract

In this paper, we use the parameterized single-step HSS (P-SHSS) iterative method to solve a broad class of singular complex symmetric linear systems. The semi-convergence properties of the P-SHSS method are derived under suitable conditions. Moreover, some properties of the preconditioned matrix and the optimal parameters are analyzed in detail. Numerical experiments are given to support our theoretical results and show the effectiveness of the P-SHSS method either as a solver or as a preconditioner.

Keywords

Complex linear systems
Iterative method
Semi-convergence
Preconditioning

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This research is supported by National Science Foundation of China (41725017), 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 (Nos. KZZD-EW-TZ-19 and KZZD-EW-TZ-15), Strategic Priority Research Program of the Chinese Academy of Sciences (XDB18010202).