Practical RPCG methods for complex symmetric linear systems

We investigate the restrictively preconditioned conjugate gradient (RPCG) method for complex symmetric linear systems. First, we transform the complex symmetric linear system into an equivalent block two-by-two linear system. Then, by making full use of the real and imaginary parts of the coefficient matrix, we construct a restrictive preconditioner with a parameter and propose a practical RPCG method for solving the complex symmetric linear systems. Finally, we analyze the spectral properties of the preconditioned matrix and give a formula for estimating the parameter. In numerical experiments, we use two examples to demonstrate the robustness and effectiveness of the practical RPCG method for solving the complex symmetric linear systems.