Two-parameter TSCSP method for solving complex symmetric system of linear equations
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We introduce a two-parameter version of the two-step scale-splitting iteration method, called TTSCSP, for solving a broad class of complex symmetric system of linear equations. We present some conditions for the convergence of the method. An upper bound for the spectral radius of the method is presented and optimal parameters which minimize this bound are given. Inexact version of the TTSCSP iteration method (ITTSCSP) is also presented. Some numerical experiments are reported to verify the effectiveness of the TTSCSP iteration method and the numerical results are compared with those of the TSCSP, the SCSP and the PMHSS iteration methods. Numerical comparison of the ITTSCSP method with the inexact version of TSCSP, SCSP and PMHSS are presented. We also compare the numerical results of the BiCGSTAB method in conjunction with the TTSCSP and the ILU preconditioners.
KeywordsComplex linear systems Symmetric positive definite MHSS PMHSS GSOR SCSP TSCSP
Mathematics Subject Classification65F10 65F50 65F08
The work of Davod Khojasteh Salkuyeh is partially supported by University of Guilan. The authors would like to thank Prof. M. Benzi and anonymous referees for their valuable comments and suggestions which greatly improved the quality of the paper.