Two-step scale-splitting method for solving complex symmetric system of linear equations
This work offers an incremental improvement to iterative solvers for complex symmetric systems, which are common in scientific computing.
The authors propose a two-step scale-splitting (TSCSP) method for solving complex symmetric linear systems, proving unconditional convergence when matrices are symmetric positive definite and computing the optimal parameter. Numerical tests show TSCSP outperforms SCSP, MHSS, PMHSS, and GSOR methods in terms of iteration counts and CPU time.
Based on the Scale-Splitting (SCSP) iteration method presented by Hezari et al. in (A new iterative method for solving a class of complex symmetric system linear of equations, Numerical Algorithms 73 (2016) 927-955), we present a new two-step iteration method, called TSCSP, for solving the complex symmetric system of linear equations $(W+iT)x=b$, where $W$ and $T$ are symmetric positive definite and symmetric positive semidefinite matrices, respectively. It is shown that if the matrices $W$ and $T$ are symmetric positive definite, then the method is unconditionally convergent. The optimal value of the parameter, which minimizes the spectral radius of the iteration matrix is also computed. Numerical {comparisons} of the TSCSP iteration method with the SCSP, the MHSS, the PMHSS and the GSOR methods are given to illustrate the effectiveness of the method.