In this paper, two methods based on generalized successive overrelaxation (GSOR) for solving weakly nonlinear systems with complex coefficient matrices are proposed: Picard-accelerated GSOR (P-AGSOR) and Picard-preconditioned GSOR (P-PGSOR) methods. Theoretical analysis demonstrates the local convergence properties of the two methods under appropriate assumptions. Numerical examples confirm the effectiveness and superiority of the two methods.

中文翻译：

---

基于GSOR的迭代方法求解具有复杂对称系数矩阵的弱非线性系统

本文提出了两种基于广义连续超松弛（GSOR）的方法来求解具有复杂系数矩阵的弱非线性系统：皮卡德加速GSOR（P-AGSOR）和皮卡德预处理GSOR（P-PGSOR）方法。理论分析证明了两种方法在适当假设下的局部收敛性。数值例子证实了这两种方法的有效性和优越性。