In this paper, we first propose a new block splitting (NBS) iteration method for solving the large sparse complex symmetric linear systems. The NBS iteration method avoids complex arithmetic compared with the combination method of real part and imaginary part (CRI) one established by Wang et al. (2017). The unconditional convergence and the quasi-optimal parameter of the NBS iteration method are given. Moreover, by further accelerating the NBS one with another parameter, we construct the parameterized BS (PBS) iteration method and establish its convergence theory. Also, the spectral properties of the PBS-preconditioned matrix are analyzed and the parameter selection strategy of the PBS iteration method is given. Numerical experiments are reported to illustrate the feasibility and effectiveness of the proposed methods.

在本文中，我们首先提出一种新的块分裂（NBS）迭代方法，用于解决大型稀疏复杂对称线性系统。与Wang等人建立的实部和虚部（CRI）组合方法相比，NBS迭代方法避免了复杂的算法。（2017）。给出了NBS迭代方法的无条件收敛和准最优参数。此外，通过进一步加速具有另一个参数的NBS，我们构造了参数化BS（PBS）迭代方法，并建立了其收敛理论。此外，分析了PBS预处理矩阵的光谱特性，并给出了PBS迭代方法的参数选择策略。数值实验表明了该方法的可行性和有效性。