Abstract In this paper, we apply the multilevel augmentation method for solving ill-posed Fredholm integral equations of the first kind via iterated Tikhonov regularization method. The method leads to fast solutions of the discrete regularization methods for the equations. The convergence rates of iterated Tikhonov regularization are achieved by using a modified parameter choice strategy. Finally, numerical experiments are given to illustrate the efficiency of the method.

中文翻译：

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多级增强方法中的参数选择

摘要 在本文中，我们通过迭代 Tikhonov 正则化方法应用多级增强方法来求解第一类不适定的 Fredholm 积分方程。该方法导致方程的离散正则化方法的快速解。迭代 Tikhonov 正则化的收敛速度是通过使用修改后的参数选择策略来实现的。最后，给出了数值实验来说明该方法的有效性。