In this paper, we modify the accelerated generalized successive overrelaxation (AGSOR) method for block two-by-two complex linear systems, and use the AGSOR method as an inner iteration for the modified Newton equations to solve the nonlinear system whose Jacobian matrix is a block two-by-two complex symmetric matrix. Our new method is named modified Newton AGSOR (MN-AGSOR) method. Because generalized successive overrelaxation (GSOR) method is a special form of the AGSOR method, the modified Newton GSOR (MN-GSOR) method is also analyzed in the discussion. Next, we use the Hölder continuous condition instead of the Lipschitz assumption to analyze and prove the local convergence properties of the MN-AGSOR method. At last, numerical experiments verify the efficiency of the MN-AGSOR method, and it can be seen from the comparison of various aspects that the MN-AGSOR method is superior to some other recently proposed methods.

中文翻译：

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修正的牛顿-AGSOR方法求解块二乘二对称对称雅可比矩阵的非线性系统

在本文中，我们修改了块二乘二复杂线性系统的加速广义连续超松弛（AGSOR）方法，并使用AGSOR方法作为改进的Newton方程的内部迭代来求解Jacobian矩阵为a的非线性系统。块二乘二的复对称矩阵。我们的新方法称为改进的牛顿AGSOR（MN-AGSOR）方法。由于广义连续超松弛（GSOR）方法是AGSOR方法的一种特殊形式，因此在讨论中还分析了改进的牛顿GSOR（MN-GSOR）方法。接下来，我们使用Hölder连续条件代替Lipschitz假设来分析和证明MN-AGSOR方法的局部收敛性。最后，数值实验验证了MN-AGSOR方法的有效性，