In this paper, we mainly discuss the iterative methods for solving nonlinear systems with complex symmetric Jacobian matrices. By applying an FPAE iteration (a fixed-point iteration adding asymptotical error) as the inner iteration of the Newton method and modified Newton method, we get the so–called Newton-FPAE method and modified Newton-FPAE method. The local and semi-local convergence properties under Lipschitz condition are analyzed. Finally, some numerical examples are given to expound the feasibility and validity of the two new methods by comparing them with some other iterative methods.

中文翻译：

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带有对称对称Jacobian矩阵的非线性系统的两种新的有效迭代方法。

在本文中，我们主要讨论求解具有对称对称雅可比矩阵的非线性系统的迭代方法。通过将FPAE迭代（增加无症状误差的定点迭代）用作Newton方法和改进的Newton方法的内部迭代，我们得到了所谓的Newton-FPAE方法和改进的Newton-FPAE方法。分析了Lipschitz条件下的局部和半局部收敛性。最后，通过一些数值例子，通过与其他迭代方法进行比较，阐述了这两种新方法的可行性和有效性。